Relevant bibliographies by topics / Mahler equations

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Mahler equations'

Author: Grafiati
Published: 28 September 2022

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Journal articles on the topic "Mahler equations"

1

Bugeaud, Yann, and Kálmán Győry. "On binomial Thue-Mahler equations." Periodica Mathematica Hungarica 49, no. 2 (December 2004): 25–34. http://dx.doi.org/10.1007/s10998-004-0520-0.

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Lalín, Matilde N. "Equations for Mahler measure and isogenies." Journal de Théorie des Nombres de Bordeaux 25, no. 2 (2013): 387–99. http://dx.doi.org/10.5802/jtnb.841.

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Dreyfus, Thomas, Charlotte Hardouin, and Julien Roques. "Hypertranscendence of solutions of Mahler equations." Journal of the European Mathematical Society 20, no. 9 (June 29, 2018): 2209–38. http://dx.doi.org/10.4171/jems/810.

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Chyzak, Frédéric, Thomas Dreyfus, Philippe Dumas, and Marc Mezzarobba. "Computing solutions of linear Mahler equations." Mathematics of Computation 87, no. 314 (July 2, 2018): 2977–3021. http://dx.doi.org/10.1090/mcom/3359.

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Nishioka, Kumiko, and Seiji Nishioka. "Autonomous equations of Mahler type and transcendence." Tsukuba Journal of Mathematics 39, no. 2 (March 2016): 251–57. http://dx.doi.org/10.21099/tkbjm/1461270059.

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Roques, Julien. "On the reduction modulo $p$ of Mahler equations." Tohoku Mathematical Journal 69, no. 1 (April 2017): 55–65. http://dx.doi.org/10.2748/tmj/1493172128.

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Kim, Dohyeong. "A modular approach to cubic Thue-Mahler equations." Mathematics of Computation 86, no. 305 (September 15, 2016): 1435–71. http://dx.doi.org/10.1090/mcom/3139.

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Nishioka, Kumiko, and Seiji Nishioka. "Algebraic theory of difference equations and Mahler functions." Aequationes mathematicae 84, no. 3 (May 11, 2012): 245–59. http://dx.doi.org/10.1007/s00010-012-0132-3.

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Bugeaud, Yann, and Kálmán Győry. "Bounds for the solutions of Thue-Mahler equations and norm form equations." Acta Arithmetica 74, no. 3 (1996): 273–92. http://dx.doi.org/10.4064/aa-74-3-273-292.

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Lalin, Matilde, and Mathew Rogers. "Functional equations for Mahler measures of genus-one curves." Algebra & Number Theory 1, no. 1 (February 1, 2007): 87–117. http://dx.doi.org/10.2140/ant.2007.1.87.

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Dissertations / Theses on the topic "Mahler equations"

1

Nguyen, Phu Qui Pierre. "Equations de Mahler et hypertranscendance." Paris 6, 2012. http://www.theses.fr/2012PA066809.

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Soit K un corps équipé d'un endomorphisme \sigma. Dans cette thèse, nous montrons que la théorie de Galois aux \sigma-différences bien connue dans le cas où \sigma est un automorphisme du corps K peut être adaptée au cas où \sigma n'est plus nécessairement surjectif, en passant à la clôture inversive de K. Nous utilisons ensuite cette théorie de Galois pour donner un critère d'indépendance algébrique pour les solutions de \sigma-équations du premier ordre. Ce résultat nous permet de caractériser les solutions hyperalgébriques de ces \sigma-équations lorsque K est muni d'une dérivation vérifiant une hypothèse de quasi-commutation avec \sigma. En appliquant notre critère d'indépendance algébrique à l'opérateur de Mahler, nous donnons enfin une preuve galoisienne d'un théorème d'hypertranscendance de Ke. Nishioka
Let K be a field equipped with an endomorphism \sigma. In this thesis, we show that the Galois theory for \sigma-difference equations, well known if \sigma is an automorphism of K, can be adapted to the case when \sigma is not necessarily surjective anymore, by passing to the inversive closure of K. We then use this Galois theory to give an algebraic independence criterion for solutions of first order \sigma-equations. This result allows us to characterize the hyperalgebraic solutions of such \sigma-equations when K is endowed with a derivation which almost commutes with \sigma. Applying our algebraic independence criterion to the Mahler operator setting, we give a galoisian proof of a hypertranscendence theorem of Ke. Nishioka
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Poulet, Marina. "Equations de Mahler : groupes de Galois et singularités régulières." Thesis, Lyon, 2021. https://tel.archives-ouvertes.fr/tel-03789627.

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Cette thèse est consacrée à l'étude des équations de Mahler et des solutions de ces équations, appelées fonctions de Mahler. Des exemples classiques de fonctions de Mahler sont les séries génératrices des suites automatiques. La première partie de cette thèse porte sur les aspects galoisiens des équations de Mahler. Notre résultat principal est un analogue pour ces équations du théorème de densité de Schlesinger selon lequel la monodromie d'une équation différentielle à points singuliers réguliers est Zariski-dense dans son groupe de Galois différentiel. Pour cela, nous commençons par attacher une paire de matrices de connexion à chaque équation de Mahler singulière régulière. Ces matrices nous permettent de construire un sous-groupe du groupe de Galois de l'équation de Mahler et nous montrons que ce sous-groupe est Zariski-dense dans le groupe de Galois. La seule hypothèse de ce théorème de densité est le caractère singulier régulier de l'équation de Mahler considérée. La deuxième partie de cette thèse est consacrée à la construction d'un algorithme qui permet de reconnaître si une équation de Mahler est singulière régulière
This thesis is devoted to the study of Mahler equations and the solutions of these equations, called Mahler functions. Classic examples of Mahler functions are the generating series of automatic sequences. The first part of this thesis deals with the Galoisian aspects of Mahler equations. Our main result is an analog for Mahler equations of the Schlesinger’s density theorem according to which the monodromy of a regular singular differential equation is Zariski-dense in its differential Galois group. To this end, we start by attaching a pair of connection matrices to each regular singular Mahler equation. These matrices enable us to construct a subgroup of the Galois group of the Mahler equation and we prove that this subgroup is Zariski-dense in the Galois group. The only assumption of this density theorem is the regular singular condition on the considered Mahler equation. The second part of this thesis is devoted to the construction of an algorithm which recognizes whether or not a Mahler equation is regular singular
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Randé, Bernard. "Equations fonctionnelles de Mahler et applications aux suites p-régulières." Bordeaux 1, 1992. https://tel.archives-ouvertes.fr/tel-01183330.

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Le concept de suite p-régulière, introduit par Allouche et Shallit, généralise celui de suite p-automatique. La série génératrice d'une telle suite est considérée, tantôt comme une série formelle, tantôt comme une fonction holomorphe (dans le cas complexe) ; elle vérifie une équation fonctionnelle linéaire, dite de Mahler. Ce travail étudie ces équations fonctionnelles de façon générale, pour les appliquer au cas particulier des suites p-régulières. Le cadre formel est celui des chapitres 1, 2 et 3. On y étudie certaines structures mahlériennes. Le chapitre 4 montre la transcendance des solutions non rationnelles, par l'étude de leurs singularités. On étend ainsi un résultat bien connu dans le cas automatique. Le chapitre 5, répondant à une question posée par Rubel, montre que, dans un cas, les solutions non rationnelles sont différentiellement transcendantes (ou hypertranscendantes). Le chapitre 7, reprenant des méthodes bien connues, s'appuie sur le chapitre 4 pour établir la transcendance des valeurs prises, s'intéressant ainsi à une question posée par Allouche et Shallit. Le chapitre 8 montre un résultat très partiel en direction d'une conjecture de Loxton et van der Poorten. Le chapitre 6 esquisse une étude dans le cas non linéaire.
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Hambrook, Kyle David. "Implementation of a Thue-Mahler equation solver." Thesis, University of British Columbia, 2011. http://hdl.handle.net/2429/38244.

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A practical algorithm for solving an arbitrary Thue-Mahler equation is presented, and its correctness is proved. Methods of algebraic number theory are used to reduce the problem of solving the Thue-Mahler equation to the problem of solving a finite collection of related Diophatine equations having parameters in an algebraic number field. Bounds on the solutions of these equations are computed by employing the theory of linear forms in logarithms of algebraic numbers. Computational Diophantine approximation techniques based on lattice basis reduction are used to reduce the upper bounds to the point where a direct enumerative search of the solution space becomes possible. Such an enumerative search is carried out with the aid of a sieving procedure to finally determine the complete set of solutions of the Thue-Mahler equation. The algorithm is implemented in full generality as a function in the Magma computer algebra system. This is the first time a completely general algorithm for solving Thue-Mahler equations has been implemented as a computer program.
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Daquila, Richard. "Strongly annular solutions to Mahler's functional equation /." The Ohio State University, 1993. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487844948075255.

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Mahlke, Jana [Verfasser]. "Validation of 360-Degree Feedback Assessments : Development, Evaluation, and Application of a Multilevel Structural Equation Model / Jana Mahlke." Berlin : Universitätsbibliothek Freie Universität Berlin, 2019. http://d-nb.info/1179782917/34.

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Book chapters on the topic "Mahler equations"

1

Von Haeseler, Fritz, and Wibke Jürgensen. "Automaticity of Solutions of Mahler Equations." In Sequences and their Applications, 228–39. London: Springer London, 1999. http://dx.doi.org/10.1007/978-1-4471-0551-0_16.

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Sprindžuk, Vladimir G. "The Thue-Mahler equation." In Lecture Notes in Mathematics, 85–110. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/bfb0073791.

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Bombieri, E. "On the thue-mahler equation." In Diophantine Approximation and Transcendence Theory, 213–43. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0078711.

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"Thue–Mahler equations." In The Algorithmic Resolution of Diophantine Equations, 117–32. Cambridge University Press, 1998. http://dx.doi.org/10.1017/cbo9781107359994.009.

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"The Thue–Mahler equation." In Exponential Diophantine Equations, 124–40. Cambridge University Press, 1986. http://dx.doi.org/10.1017/cbo9780511566042.013.

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"Differential equations for families of Mahler measures." In Many Variations of Mahler Measures, 62–72. Cambridge University Press, 2020. http://dx.doi.org/10.1017/9781108885553.006.

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Loeckx, J., and H. D. Ehrich. "Algebraic specification of abstract data types." In Handbook of Logic in Computer Science: Volume 5. Algebraic and Logical Structures. Oxford University Press, 2001. http://dx.doi.org/10.1093/oso/9780198537816.003.0007.

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It is widely accepted that the quality of software can be improved if its design is systematically based on the principles of modularization and formalization. Modularization consists in replacing a problem by several “smaller” ones. Formalization consists in using a formal language; it obliges the software designer to be precise and principally allows a mechanical treatment. One may distinguish two modularization techniques for the software design. The first technique consists in a modularization on the basis of the control structures. It is used in classical programming languages where it leads to the notion of a procedure. Moreover, it is used in “imperative” specification languages such as VDM [Woodman and Heal, 1993; Andrews and Ince, 1991], Raise [Raise Development Group, 1995], Z [Spivey, 1989] and B [Abrial, 1996]. The second technique consists in a modularization on the basis of the data structures. While modern programming languages such as Ada [Barstow, 1983] and ML [Paulson, 1991] provide facilities for this modularization technique, its systematic use leads to the notion of abstract data types. This technique is particularly interesting in the design of software for non-numerical problems. Compared with the first technique it is more abstract in the sense that algebras are more abstract than algorithms; in fact, control structures are related to algorithms whereas data structures are related to algebras. Formalization leads to the use of logic. The logics used are generally variants of the equational logic or of the first-order predicate logic. The present chapter is concerned with the specification of abstract data types. The theory of abstract data type specification is not trivial, essentially because the objects considered — viz. algebras — have a more complex structure than, say, integers. For more clarity the present chapter treats algebras, logics, specification methods (“specification-in-the-small”), specification languages (“specification-in-the-large”) and parameterization separately. In order to be accessible to a large number of readers it makes use of set-theoretical notions only. This contrasts with a large number of publications on the subject that make use of category theory [Ehrig and Mahr, 1985; Ehrich et al., 1989; Sannella and Tarlecki, 2001].
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