On the rankin-selberg problem

Web1 de jan. de 1989 · The Rankin-Selberg method gives an improvement over the “trivial estimate”.. ... Langlands, R. “Problems in the theory of automorphic forms,” In: Springer Lecture Notes in Mathematics. 170 (1970). Google Scholar. 55. Littlewood, D. The Theory of Group Characters, second edition. WebKeywords: Rankin-Selberg problem, Riesz mean, Vorono¨ı type formula, power moment MSC(2000): 11N37, 11F30 1 Introduction Letϕ(z) be a holomorphiccusp form ofweight κ with respect to the full modular group SL2(Z), and denote by a(n)then-th Fourier coefficient of ϕ(z). Suppose that ϕ(z) is normalized such

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WebThe Rankin-Selberg L-function of the pair F, G= complex conjugate of G, is the Dirichlet series L(s,F⊗G) = ζ(2s) X n≥1 a n b n n 1−k−s. (1.7) Its analytic continuation and functional equation were established separately by Rankin [17] and Selberg [18]. The proof depends on properties of the non-holomorphic Eisenstein series E s(z) = π ... WebPub Date: February 2024 arXiv: arXiv:2002.00591 Bibcode: 2024arXiv200200591H Keywords: Mathematics - Number Theory; E-Print: 28 pages. how to say indigent https://paramed-dist.com

On the Rankin-Selberg problem in short intervals - NASA/ADS

WebThis is a horizontal analogue of a well-known result of Cornut and Vatsal [Nontriviality of Rankin-Selberg L-functions and CM points, L-functions and Galois representations, vol. 320, Cambridge Univ. Press, Cambridge, 2007, pp. 121–186]. Web1 de jul. de 1999 · On Riesz means of the coefficients of the Rankin–Selberg series - Volume 127 Issue 1. Skip to main content Accessibility help ... On some mean square estimates in the Rankin-Selberg problem. Applicable Analysis and Discrete Mathematics, Vol. 1, Issue. 1, p. 111. CrossRef; http://www.math.keio.ac.jp/~kurihara/PANT2024/PANT2/PANTSlides/BingrongHuang.pdf how to say indigestion in spanish

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On the rankin-selberg problem

Transactions of the American Mathematical Society Series B

WebIvić A, Matsumoto K, Tanigawa Y. On Riesz means of the coefficients of the Rankin-Selberg series. Math Proc Camb Phil Soc, 127: 117–131 (1999) Article MATH Google … WebScience in China A: Mathematics. Pub Date: January 2008 DOI: 10.1007/s11425-007-0130-4 arXiv: arXiv:0805.1975

On the rankin-selberg problem

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WebRankin [25] and Selberg [26] invented the powerful Rankin–Selberg method, and then successfully showed that 2(X,φ) φ X3/5. This bound remains the best since it was proved … WebON THE RANKIN–SELBERG PROBLEM BINGRONG HUANG Abstract. In this paper, we solve the Rankin–Selberg problem. That is, we break the well known Rankin–Selberg’s …

http://www.doiserbia.nb.rs/img/doi/1452-8630/2007/1452-86300701111I.pdf WebRankin-Selberg bound ∆(x) ˝ε x3/5+ε. Clearly improvement will come from better values of θ. Note that the best possible value of θin (3.2) is θ= 1, which follows from general results on Dirichlet series (see e.g., [3, Chapter 9]). It gives 1/2+εas the exponent in the Rankin-Selberg problem, which is the limit of the

Web27 de abr. de 2014 · Given two unitary automorphic cuspidal representations and defined on and , respectively, with and being Galois extensions of , we consider two generalized Rankin-Selberg -functions obtained by forcefully factoring and . We prove the absolute convergence of these -functions for . The main difficulty in our case is that the two … WebVol. 90 (2008) On the fourth moment in the Rankin-Selberg problem 413 The constant C(> 0) in (1.1) may be written down explicitly (see e.g., [7]), and c n is the convolution …

WebOn the Rankin{Selberg problem Bingrong Huang Shandong University Dec. 09, 2024 PANT - Kyoto 2024 @ RIMS, Kyoto University. Contents 1 Arithmetic functions 2 The Rankin{Selberg theorem 3 The Friedlander{Iwaniec theorem 4 The Rankin{Selberg problem and main result 5 Analytic twisted sum of GL(3) Fourier coe cients

WebTHE RANKIN-SELBERG PROBLEM Aleksandar Ivic An overview of the classical Rankin-Selberg problem involving the asymp-totic formula for sums of coefficients of … north italia green hills menunorth italia in king of prussiahttp://homepage.math.uiowa.edu/~yey/papers/gafa2002.pdf how to say indonesia in spanishWeb7 de set. de 2011 · Comments: 12 pages: Subjects: Number Theory (math.NT) MSC classes: : 11N37, 44A15, 26A12: Journal reference: Moscow Journal of Combinatorics … north italia irvine spectrumWebadshelp[at]cfa.harvard.edu The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A how to say indomitableWebOn the Rankin-Selberg problem. Abstract: In this talk, I will introduce a method to solve the Rankin-Selberg problem on the second moment of Fourier coefficients of a GL(2) Hecke eigenform. This improves the classical result 3/5 of Rankin and Selberg (in 1939/1940). If time permit, a sketch of proof and some other results will also be presented. north italia king of prussia reviewsWeb13 de mai. de 2005 · Let f and g be two primitive (holomorphic or Maass) cusp forms of arbitrary level, character and infinity parameter by which we mean the weight in the holomorphic case and the spectral parameter in the Maass case. Let L(s,f × g) be the associated Rankin-Selberg L-function.If g is fixed and the infinity parameter μf of f … north italia king of prussia mall