Relevant bibliographies by topics / Conjecture de Littlewood

Academic literature on the topic 'Conjecture de Littlewood'

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Published: 13 July 2024

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Journal articles on the topic "Conjecture de Littlewood"

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Mignot, Teddy. "Points de hauteur bornée sur les hypersurfaces lisses de l'espace triprojectif." International Journal of Number Theory 11, no. 03 (March 31, 2015): 945–95. http://dx.doi.org/10.1142/s1793042115500529.

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Nous démontrons ici la conjecture de Batyrev et Manin pour le nombre de points de hauteur bornée de certaines hypersurfaces de l'espace triprojectif de tridegré (1, 1, 1). La constante intervenant dans le résultat final est celle conjecturée par Peyre. La méthode utilisée est inspirée de celle développée par Schindler pour traiter le cas des hypersurfaces des espaces biprojectifs. Celle-ci est essentiellement basée sur la méthode du cercle de Hardy–Littlewood. We prove the Batyrev–Manin conjecture for the number of points of bounded height on some smooth hypersurfaces of the triprojective space of tridegree (1, 1, 1). The constant appearing in the final result is the one conjectured by Peyre. The method used is the one developed by Schindler to study the case of hypersurfaces of biprojective spaces. It is essentially based on the Hardy–Littlewood method.
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Haglund, J., J. Morse, and M. Zabrocki. "A Compositional Shuffle Conjecture Specifying Touch Points of the Dyck Path." Canadian Journal of Mathematics 64, no. 4 (August 1, 2012): 822–44. http://dx.doi.org/10.4153/cjm-2011-078-4.

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Abstract We introduce a q, t-enumeration of Dyck paths that are forced to touch the main diagonal at specific points and forbidden to touch elsewhere and conjecture that it describes the action of the Macdonald theory ∇ operator applied to a Hall–Littlewood polynomial. Our conjecture refines several earlier conjectures concerning the space of diagonal harmonics including the “shuffle conjecture” (Duke J. Math. 126 (2005), pp. 195 − 232) for ∇ en[X]. We bring to light that certain generalized Hall–Littlewood polynomials indexed by compositions are the building blocks for the algebraic combinatorial theory of q, t-Catalan sequences, and we prove a number of identities involving these functions.
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CHAN, TSZ HO. "A NOTE ON PRIMES IN SHORT INTERVALS." International Journal of Number Theory 02, no. 01 (March 2006): 105–10. http://dx.doi.org/10.1142/s1793042106000437.

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Montgomery and Soundararajan obtained evidence for the Gaussian distribution of primes in short intervals assuming a quantitative Hardy–Littlewood conjecture. In this article, we show that their methods may be modified and an average form of the Hardy–Littlewood conjecture suffices.
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Xuan Jiang, Chun. "On the singular series in the Jiang prime k-tuple theorem." Physics & Astronomy International Journal 2, no. 6 (November 16, 2018): 514–17. http://dx.doi.org/10.15406/paij.2018.02.00134.

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Using Jiang function we prove Jiang prime k-tuple theorem. We find true singular series. Using the examples we prove the Hardy-Littlewood prime k-tuple conjecture with wrong singular series. Jiang prime k-tuple theorem will replace the Hardy-Littlewood prime k-tuple conjecture.
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Chindris, Calin, Harm Derksen, and Jerzy Weyman. "Counterexamples to Okounkov’s log-concavity conjecture." Compositio Mathematica 143, no. 6 (November 2007): 1545–57. http://dx.doi.org/10.1112/s0010437x07003090.

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de Mathan, Bernard. "Conjecture de Littlewood et récurrences linéaires." Journal de Théorie des Nombres de Bordeaux 15, no. 1 (2003): 249–66. http://dx.doi.org/10.5802/jtnb.401.

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Brüdern, Jörg. "On Waring's problem for cubes." Mathematical Proceedings of the Cambridge Philosophical Society 109, no. 2 (March 1991): 229–56. http://dx.doi.org/10.1017/s0305004100069711.

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A classical conjecture in the additive theory of numbers is that all sufficiently large natural numbers may be written as the sum of four positive cubes of integers. This is known as the Four Cubes Problem, and since the pioneering work of Hardy and Littlewood one expects a much more precise quantitative form of the conjecture to hold. Let v(n) be the number of representations of n in the proposed manner. Then the expected formula takes the shapewhere (n) is the singular series associated with four cubes as familiar in the Hardy–Littlewood theory.
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BUGEAUD, YANN, ALAN HAYNES, and SANJU VELANI. "METRIC CONSIDERATIONS CONCERNING THE MIXED LITTLEWOOD CONJECTURE." International Journal of Number Theory 07, no. 03 (May 2011): 593–609. http://dx.doi.org/10.1142/s1793042111004289.

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The main goal of this paper is to develop a metrical theory of Diophantine approximation within the framework of the de Mathan–Teulié Conjecture — also known as the "Mixed Littlewood Conjecture". Let p be a prime. A consequence of our main result is that, for almost every real number α, [Formula: see text]
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Krass, S. "On a conjecture of Littlewood in Diophantine approximations." Bulletin of the Australian Mathematical Society 32, no. 3 (December 1985): 379–87. http://dx.doi.org/10.1017/s0004972700002495.

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A conjecture of Littlewood States that for arbitrary , and any ε > 0 there exist m0 ≠ 0, m1,…,mn so that . In this paper we show this conjecture holds for all ξ̲ = (ξ1,…,ξn) such that 1, ξ1,…,ξn is a rational bass of a real algebraic number field of degree n+1.
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Klemes, Ivo. "A Note on Hardy's Inequality." Canadian Mathematical Bulletin 36, no. 4 (December 1, 1993): 442–48. http://dx.doi.org/10.4153/cmb-1993-059-4.

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Dissertations / Theses on the topic "Conjecture de Littlewood"

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Keliher, Liam. "Results and conjectures related to the sharp form of the Littlewood conjecture." Thesis, McGill University, 1995. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=23402.

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Let $0
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Trudeau, Sidney. "On a special case of the Strong Littlewood conjecture." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0002/MQ44303.pdf.

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Hinkel, Dustin. "Constructing Simultaneous Diophantine Approximations Of Certain Cubic Numbers." Diss., The University of Arizona, 2014. http://hdl.handle.net/10150/338879.

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For K a cubic field with only one real embedding and α, β ϵ K, we show how to construct an increasing sequence {m_n} of positive integers and a subsequence {ψ_n} such that (for some constructible constants γ₁, γ₂ > 0): max{ǁm_nαǁ,ǁm_nβǁ} < [(γ₁)/(m_n^(¹/²))] and ǁψ_nαǁ < γ₂/[ψ_n^(¹/²) log ψ_n] for all n. As a consequence, we have ψ_nǁψ_nαǁǁψ_nβǁ < [(γ₁ γ₂)/(log ψ_n)] for all n, thus giving an effective proof of Littlewood's conjecture for the pair (α, β). Our proofs are elementary and use only standard results from algebraic number theory and the theory of continued fractions.
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Sanders, Tom. "Topics in arithmetic combinatorics." Thesis, University of Cambridge, 2007. https://www.repository.cam.ac.uk/handle/1810/236994.

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This thesis is chiefly concerned with a classical conjecture of Littlewood's regarding the L¹-norm of the Fourier transform, and the closely related idem-potent theorem. The vast majority of the results regarding these problems are, in some sense, qualitative or at the very least infinitary and it has become increasingly apparent that a quantitative state of affairs is desirable. Broadly speaking, the first part of the thesis develops three new tools for tackling the problems above: We prove a new structural theorem for the spectrum of functions in A(G); we extend the notion of local Fourier analysis, pioneered by Bourgain, to a much more general structure, and localize Chang's classic structure theorem as well as our own spectral structure theorem; and we refine some aspects of Freiman's celebrated theorem regarding the structure of sets with small doubling. These tools lead to improvements in a number of existing additive results which we indicate, but for us the main purpose is in application to the analytic problems mentioned above. The second part of the thesis discusses a natural version of Littlewood's problem for finite abelian groups. Here the situation varies wildly with the underlying group and we pay special attention first to the finite field case (where we use Chang's Theorem) and then to the case of residues modulo a prime where we require our new local structure theorem for A(G). We complete the consideration of Littlewood's problem for finite abelian groups by using the local version of Chang's Theorem we have developed. Finally we deploy the Freiman tools along with the extended Fourier analytic techniques to yield a fully quantitative version of the idempotent theorem.
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Dehnert, Fabian. "The distribution of rational points on some projective varieties." Doctoral thesis, 2019. http://hdl.handle.net/21.11130/00-1735-0000-0005-12EB-E.

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Book chapters on the topic "Conjecture de Littlewood"

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Yamasaki, Yoshinori. "Ramanujan Cayley Graphs of the Generalized Quaternion Groups and the Hardy–Littlewood Conjecture." In Mathematical Modelling for Next-Generation Cryptography, 159–75. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-5065-7_9.

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Qin, Hourong. "The Mazur Conjecture, the Lang-Trotter Conjecture and the Hardy-Littlewood Conjecture." In Forty Years of Algebraic Groups, Algebraic Geometry, and Representation Theory in China, 315–29. WORLD SCIENTIFIC, 2022. http://dx.doi.org/10.1142/9789811263491_0016.

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Conference papers on the topic "Conjecture de Littlewood"

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Bugeaud, Yann, Bernard de Mathan, and Takao Komatsu. "On a mixed Littlewood conjecture in fields of power series." In DIOPHANTINE ANALYSIS AND RELATED FIELDS: DARF 2007/2008. AIP, 2008. http://dx.doi.org/10.1063/1.2841906.

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