Relevant bibliographies by topics / Automorphic periods

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Automorphic periods'

Author: Grafiati
Published: 5 April 2025

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Journal articles on the topic "Automorphic periods"

1

Jacquet, Hervé, Erez Lapid, and Jonathan Rogawski. "Periods of automorphic forms." Journal of the American Mathematical Society 12, no. 1 (1999): 173–240. http://dx.doi.org/10.1090/s0894-0347-99-00279-9.

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Frahm, Jan, and Feng Su. "Upper bounds for geodesic periods over rank one locally symmetric spaces." Forum Mathematicum 30, no. 5 (September 1, 2018): 1065–77. http://dx.doi.org/10.1515/forum-2017-0185.

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AbstractWe prove upper bounds for geodesic periods of automorphic forms over general rank one locally symmetric spaces. Such periods are integrals of automorphic forms restricted to special totally geodesic cycles of the ambient manifold and twisted with automorphic forms on the cycles. The upper bounds are in terms of the Laplace eigenvalues of the two automorphic forms, and they generalize previous results for real hyperbolic manifolds to the context of all rank one locally symmetric spaces.
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Zelditch, Steven. "geodesic periods of automorphic forms." Duke Mathematical Journal 56, no. 2 (April 1988): 295–344. http://dx.doi.org/10.1215/s0012-7094-88-05613-x.

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Yamana, Shunsuke. "Periods of residual automorphic forms." Journal of Functional Analysis 268, no. 5 (March 2015): 1078–104. http://dx.doi.org/10.1016/j.jfa.2014.11.009.

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Ichino, Atsushi, and Shunsuke Yamana. "Periods of automorphic forms: the case of." Compositio Mathematica 151, no. 4 (November 13, 2014): 665–712. http://dx.doi.org/10.1112/s0010437x14007362.

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Following Jacquet, Lapid and Rogawski, we define a regularized period of an automorphic form on $\text{GL}_{n+1}\times \text{GL}_{n}$ along the diagonal subgroup $\text{GL}_{n}$ and express it in terms of the Rankin–Selberg integral of Jacquet, Piatetski-Shapiro and Shalika. This extends the theory of Rankin–Selberg integrals to all automorphic forms on $\text{GL}_{n+1}\times \text{GL}_{n}$.
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Lee, Min Ho. "Mixed automorphic forms and differential equations." International Journal of Mathematics and Mathematical Sciences 13, no. 4 (1990): 661–68. http://dx.doi.org/10.1155/s0161171290000916.

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We construct mixed automorphic forms associated to a certain class of nonhomogeneous linear ordinary differential equations. We also establish an isomorphism between the space of mixed automorphic forms of the second kind modulo exact forms nd a certain parabolic cohomology explicitly in terms of the periods of mixed automorphic forms.
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Daughton, Austin. "A Hecke correspondence theorem for automorphic integrals with infinite log-polynomial sum period functions." International Journal of Number Theory 10, no. 07 (September 9, 2014): 1857–79. http://dx.doi.org/10.1142/s1793042114500596.

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We generalize the correspondence between Dirichlet series with finitely many poles that satisfy a functional equation and automorphic integrals with log-polynomial sum period functions. In particular, we extend the correspondence to hold for Dirichlet series with finitely many essential singularities. We also study Dirichlet series with infinitely many poles in a vertical strip. For Hecke groups with λ ≥ 2 and some weights, we prove a similar correspondence for these Dirichlet series. For this case, we provide a way to estimate automorphic integrals with infinite log-polynomial periods by automorphic integrals with finite log-polynomial periods.
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Yamana, Shunsuke. "PERIODS OF AUTOMORPHIC FORMS: THE TRILINEAR CASE." Journal of the Institute of Mathematics of Jussieu 17, no. 1 (October 26, 2015): 59–74. http://dx.doi.org/10.1017/s1474748015000377.

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Following Jacquet, Lapid and Rogawski, we regularize trilinear periods. We use the regularized trilinear periods to compute Fourier–Jacobi periods of residues of Eisenstein series on metaplectic groups, which has an application to the Gan–Gross–Prasad conjecture.
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ZYDOR, Michal. "Periods of automorphic forms over reductive subgroups." Annales scientifiques de l'École Normale Supérieure 55, no. 1 (2022): 141–83. http://dx.doi.org/10.24033/asens.2493.

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Sharp, Richard. "Closed Geodesics and Periods of Automorphic Forms." Advances in Mathematics 160, no. 2 (June 2001): 205–16. http://dx.doi.org/10.1006/aima.2001.1987.

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Dissertations / Theses on the topic "Automorphic periods"

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Daughton, Austin James Chinault. "Hecke Correspondence for Automorphic Integrals with Infinite Log-Polynomial Periods." Diss., Temple University Libraries, 2012. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/162078.

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Mathematics
Ph.D.
Since Hecke first proved his correspondence between Dirichlet series with functional equations and automorphic forms, there have been a great number of generalizations. Of particular interest is a generalization due to Bochner that gives a correspondence between Dirichlet series with any finite number of poles that satisfy the classical functional equation and automorphic integrals with (finite) log-polynomial sum period functions. In this dissertation, we extend Bochner's result to Dirichlet series with finitely many essential singularities. With some restrictions on the underlying group and the weight, we also prove a correspondence for Dirichlet series with infinitely many poles. For this second correspondence, we provide a technique to approximate automorphic integrals with infinite log-polynomial sum period functions by automorphic integrals with finite log-polynomial period functions.
Temple University--Theses
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Menes, Thibaut. "Grandes valeurs des formes de Maass sur des quotients compacts de grassmanniennes hyperboliques dans l’aspect volume." Electronic Thesis or Diss., Paris 13, 2024. http://www.theses.fr/2024PA131059.

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Soient n > m = 1 des entiers tels que n + m >= 4 soit pair. On prouve l’existence, dans l’aspect volume, de formes de Maass exceptionnelles sur des quotients compacts de la grassmanienne hyperbolique de signature (n,m). La méthode repose sur le travail de Rudnick et Sarnak, étendu par Donnelly puis généralisé par Brumley et Marshall en rang supérieur. Celle-ci combine un argument de comptage et une relation de périodes permettant de montrer qu’une certaine période distingue les relèvements thêta depuis un groupe auxiliaire. La structure de niveau est définie relativement à cette période et le groupe auxiliaire qui intervient est U(m,m) ou Sp_2m(R), de sorte que (U(n,m),U(m,m)) ou (O(n,m),Sp_2m(R)) soit une paire duale réductive de type 1. La borne inférieure s’exprime naturellement, à un facteur logarithmique près, comme le quotient des volumes avec la structure de congruence principale sur le groupe auxiliaire
Let n > m = 1 be integers such that n + m >= 4 is even. We prove the existence, in the volume aspect, of exceptional Maass forms on compact quotients of the hyperbolic Grassmannian of signature (n,m). The method builds upon the work of Rudnick and Sarnak, extended by Donnelly and then generalized by Brumley and Marshall to higher rank. It combines a counting argument with a period relation, showingthat a certain period distinguishes theta lifts from an auxiliary group. The congruence structure is defined with respect to this period and the auxiliary group is either U(m,m) or Sp_2m(R), making (U(n,m),U(m,m)) or (O(n,m),Sp_2m(R)) a type 1 dual reductive pair. The lower bound is naturally expressed, up to a logarithmic factor, as the ratio of the volumes, with the principal congruence structure on the auxiliary group
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Corbett, Andrew James. "Period integrals and L-functions in the theory of automorphic forms." Thesis, University of Bristol, 2017. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.723463.

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Dimbour, William. "Solutions presque automorphes et S asymptotiquement ω– périodiques pour une classe d’équations d’évolution." Thesis, Antilles-Guyane, 2013. http://www.theses.fr/2013AGUY0599/document.

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Ce travail de thèse est consacré à l’étude d’équations d’évolution et d’équations différentielles à argument constant par morceaux. L’étude des équations différentielles à argument constant par morceaux est un domaine important car ces équations ont la structure de système dynanmique de longueur constante. La continuité des solutions conduit à une relation de récurrence entre les valeurs de cette dernière entre les points n et n+1, où n est un entier relatif quelconque. Par conséquent les équations différentielles à argument constant par morceaux combinent à la fois les propriétés des équations différentielles et des équations aux différences. Nous étudierons l’existence de solutions presque automorphes et S-asymptotiquement omega-périodiques d’équations d’évolutions et d’équations à argument constant par morceaux. L’étude de solutions presque automorphes et S’asymptotiquement omega periodiques est motivé par le fait que ces fonctions généralisent celle des fonctions périodiques. Nous obtiendrons donc des résultats concernant l’existence et l’unicité de solutions presque automorphes et S asymptotiquement omega périodiques de plusieurs équations d’évolutions. Cette problématique sera notamment étudiée dans le cadre des équations d’évolutions appartenant à la classe des équations différentielles à argument constant par morceaux
This thesis deals with the study of evolution equations and differential equations with piecewise constant argument. Studies of such equations were motivated by the fact that they represent a hybrid of discrete and continuous dynamical systems and combine the properties of both differential and differential-difference equations. We study the existence of almost automorphic solutions and S asymptotically omega periodic solution of evolution equations and differential equations with piecewise constant argument. The study of almost automorphic and S asymptotically omega periodic functions is motivated by the fact that these functions generalize the concept of periodic functions. Therefore, we obtain results about existence and unicity of almost automorphic and S asymptotic omega periodic solution of evolution equations. We will study this problem considering evolution equations who belong to a class of differential equation with piecewise constant argument
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Boudjema, Souhila. "OSCILLATIONS DANS DES ÉQUATIONS DE LIÉNARD ET DES ÉQUATIONS D'ÉVOLUTION SEMI-LINÉAIRES." Phd thesis, Université Panthéon-Sorbonne - Paris I, 2013. http://tel.archives-ouvertes.fr/tel-00903302.

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Dans ce travail, on étudier, au voisinage d'un point d'équilibre, l'existence et l'unicité et la dépendance régulière des solutions presque-périodique (p.p.), présqu'automorphe (p.a.), asymptotiquement p.p., asymptotiquement p.a., pseudo p.p., pseudo p.a., pseudo p.p. avec poids, pseudo p.a. avec poids de la famille d'équations de Liénard forcée suivantes x''(t) + f(x(t), p). x'(t) + g(x(t), p) = ep(t), (1) où le terme ep est de la même nature que la solution, et p est un paramètre dans un espace de Banach. On utilise le théorème des fonctions implicites au voisinage de l'équilibre. On étudier aussi deux cas particuliers de la famille (1) qui sont x''(t) + f1(x(t)). x'(t) + g1(x(t))= e(t), x''(t) + f2(x(t), q). x'(t) + g2(x(t), q) = e(t). On établit aussi un nouveau résultat sur la dépendance différentielle des solutions S-asymptotiquement presque-périodique du problème de Cauchy x'(t)=A(t) x(t)+f(t, x(t),u(t) ) x(0) = ζ , par rapport à la condition initial et le contrôle u. On applique cet résultat sur une équation parabolique avec coefficients périodique par rapport au temps.
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Walls, Patrick. "The Theta Correspondence and Periods of Automorphic Forms." Thesis, 2013. http://hdl.handle.net/1807/43752.

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The study of periods of automorphic forms using the theta correspondence and the Weil representation was initiated by Waldspurger and his work relating Fourier coefficients of modular forms of half-integral weight, periods over tori of modular forms of integral weight and special values of L-functions attached to these modular forms. In this thesis, we show that there are general relations among periods of automorphic forms on groups related by the theta correspondence. For example, if G is a symplectic group and H is an orthogonal group over a number field k, these relations are identities equating Fourier coefficients of cuspidal automorphic forms on G (relative to the Siegel parabolic subgroup) and periods of cuspidal automorphic forms on H over orthogonal subgroups. These identities are quite formal and follow from the basic properties of theta functions and the Weil representation; further study is required to show how they compare to the results of Waldspurger. The second part of this thesis shows that, under some restrictions, the identities alluded to above are the result of a comparison of nonstandard relative traces formulas. In this comparison, the relative trace formula for H is standard however the relative trace formula for G is novel in that it involves the trace of an operator built from theta functions. The final part of this thesis explores some preliminary results on local height pairings of special cycles on the p-adic upper half plane following the work of Kudla and Rapoport. These calculations should appear as the local factors of arithmetic orbital integrals in an arithmetic relative trace formula built from arithmetic theta functions as in the work of Kudla, Rapoport and Yang. Further study is required to use this approach to relate Fourier coefficients of modular forms of half-integral weight and arithmetic degrees of cycles on Shimura curves (which are the analogues in the arithmetic situation of the periods of automorphic forms over orthogonal subgroups).
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Books on the topic "Automorphic periods"

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D, Goldfeld, ed. Collected works of Hervé Jacquet. Providence, R.I: American Mathematical Society, 2011.

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N'Guerekata, Gaston M. Almost Automorphic and Almost Periodic Functions in Abstract Spaces. Boston, MA: Springer US, 2001.

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1938-, Griffiths Phillip, and Kerr Matthew D. 1975-, eds. Hodge theory, complex geometry, and representation theory. Providence, Rhode Island: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 2013.

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Periods and Harmonic Analysis on Spherical Varieties. Societe Mathematique De France, 2018.

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Diagana, Toka. Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces. Springer, 2013.

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Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces. Springer, 2013.

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Diagana, Toka. Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces. Springer, 2015.

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Diagana, Toka. Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces. Springer London, Limited, 2013.

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Nekrashevych, Volodymyr. Groups and Topological Dynamics. American Mathematical Society, 2022.

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Groups and Topological Dynamics. American Mathematical Society, 2022.

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Book chapters on the topic "Automorphic periods"

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Dou, Ze-Li, and Qiao Zhang. "Periods of automorphic forms." In Six Short Chapters on Automorphic Forms and L-functions, 17–42. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28708-4_2.

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Shimura, Goro. "Automorphic forms and the periods of abelian varieties." In Collected Papers, 115–46. New York, NY: Springer New York, 2003. http://dx.doi.org/10.1007/978-1-4612-2060-2_4.

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Shimura, Goro. "The periods of certain automorphic forms of arithmetic type." In Collected Papers, 360–87. New York, NY: Springer New York, 2003. http://dx.doi.org/10.1007/978-1-4612-2060-2_12.

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Cornelissen, Gunther, and Oliver Lorscheid. "Toroidal Automorphic Forms, Waldspurger Periods and Double Dirichlet Series." In Multiple Dirichlet Series, L-functions and Automorphic Forms, 131–46. Boston, MA: Birkhäuser Boston, 2012. http://dx.doi.org/10.1007/978-0-8176-8334-4_6.

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Dou, Ze-Li, and Qiao Zhang. "Theta lifts and periods with respect to a quadratic extension." In Six Short Chapters on Automorphic Forms and L-functions, 99–123. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28708-4_6.

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Shimura, Goro. "On the critical values of certain Dirichlet series and the periods of automorphic forms." In Collected Papers, 848–908. New York, NY: Springer New York, 2003. http://dx.doi.org/10.1007/978-1-4612-2060-2_23.

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N’Guérékata, Gaston M. "Almost Automorphic Functions." In Almost Periodic and Almost Automorphic Functions in Abstract Spaces, 17–35. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-73718-4_2.

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Diagana, Toka. "Almost Automorphic Functions." In Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, 111–40. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00849-3_4.

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Getz, Jayce R., and Heekyoung Hahn. "Distinction and Period Integrals." In An Introduction to Automorphic Representations, 371–94. Cham: Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-41153-3_14.

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Diagana, Toka. "Pseudo-Almost Automorphic Functions." In Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, 167–88. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00849-3_6.

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Conference papers on the topic "Automorphic periods"

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Li, Lan. "Existence of Almost Periodic and Almost Automorphic Solutions for Second Order Differential Equations." In 2011 Seventh International Conference on Computational Intelligence and Security (CIS). IEEE, 2011. http://dx.doi.org/10.1109/cis.2011.332.

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Arneodo, A., F. Argoul, and P. Richetti. "Symbolic dynamics in the Belousov-Zhabotinskii reaction: from Rössler’s intuition to experimental evidence for Shil’nikov homoclinic chaos." In Nonlinear Dynamics in Optical Systems. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/nldos.1990.is2.

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The Belousov-Zhabotinskii reaction has revealed most of the well-known scenarios to chaos including period-doubling, intermittency, quasiperiodicity, frequency locking, fractal torus …. However, although the data have been shown to display unambiguous features of deterministic chaos, the understanding of the nature and the origin of the observed behavior has been incomplete. In 1976, Rössler suggested an intuitive interpretation to explain chemical chaos. His feeling was that nonperiodic wandering trajectories might arise in chemical systems from a pleated slow manifold (Fig. 1a), if the flow on the lower surface of the pleat had the property of returning trajectories to a small neighborhood of an unstable focus lying on the upper surface. In this communication, we intend to revisit the terminology introduced by Rössler of “spiral-type”, “screw-type” and “funnel-type” strange attractors in terms of chaotic orbits that occur in nearly homoclinic conditions. According to a theorem by Shil’nikov, there exist uncountably many nonperiodic trajectories in systems which display a homoclinic orbit biasymptotic to a saddle-focus O, providing the following condition is fulfilled: ρ/λ < 1, where the eigenvalue of O are (−λ, ρ ± iω). This subset of chaotic trajectories is actually in one to one correspondance with a shift automorphism with an infinite number of symbols. Since homoclinic orbits are structurally unstable objects which lie on codimension-one hypersurfaces in the constraint space, one can reasonably hope to cross these hypersurfaces when following a one-parameter path. The bifurcation structure encountered near homoclinicity involves infinite sequences of saddle-node and period-doubling bifurcations. The aim of this paper is to provide numerical and experimental evidences for Shil’nikov homoclinic chaos in nonequilibrium chemical systems.
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