On the rankin-selberg problem

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August undefined, 2024

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 … Web1 de dez. de 2024 · In particular, Wu [55] has shown that n≤x λ f (n) In 1930s, Rankin [42] and Selberg [46] independently proved the following asymptotic formula where c f is a …

[2002.00591v2] On the Rankin--Selberg problem

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; WebOn 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. simplinic berlin

On the nonnegativity of Rankin-Selberg L-functions at the center …

WebIMRN International Mathematics Research Notices 2003,No. 2 On the Nonnegativity of Rankin-Selberg L-Functions at the Center of Symmetry Erez M. Lapid 1 Introduction Let π be a self-dual cuspidal representation of GLn(A) where A is the ring of adeles of` a number ﬁeld F.Thenπ is either symplectic or orthogonal,that is,exactly one of the Web26 de out. de 2024 · In this paper, by assuming the generalized Lindel\"of hypothesis, we study the Rankin-Selberg problem in families of holomorphic modular forms. By using … Web2 BINGRONGHUANG This bound remains the best since it was born for more than 80 years. The Rankin–Selberg problem is to improve the exponent 3/5. simplinity solutions private limited

ON SOME MEAN SQUARE ESTIMATES IN THE RANKIN-SELBERG PROBLEM

On the rankin-selberg problem

Web6 de abr. de 2024 · DOI: 10.1007/s12044-023-00733-7 Corpus ID: 258020156; The second moment of the Fourier coefficients of triple product $${\varvec{L}}$$-functions @article{2024TheSM ... Web14 de mai. de 2008 · Key Words: The Rankin-Selberg problem, Riesz mean, Vorono ¨ ı type formula, Pow er moment. This work is supported by National Natural Science …

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Web3 de fev. de 2024 · Please join the Simons Foundation and our generous member organizations in supporting arXiv during our giving campaign September 23-27. 100% … 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].

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 … WebScience in China A: Mathematics. Pub Date: January 2008 DOI: 10.1007/s11425-007-0130-4 arXiv: arXiv:0805.1975

WebIn this paper, by assuming the generalized Lindelöf hypothesis, we study the Rankin-Selberg problem in families of holomorphic modular forms. By using the Lindelöf-on … 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

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 …

Web7 de set. de 2011 · Comments: 12 pages: Subjects: Number Theory (math.NT) MSC classes: : 11N37, 44A15, 26A12: Journal reference: Moscow Journal of Combinatorics … rayner manufacturingWebRankin [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 … rayner montgomeryWebTHE SUBCONVEXITY PROBLEM FOR RANKIN-SELBERG L FUNCTIONS. 3 for 0, the implied constant depending on ε,s,gand the parameters at inﬁnity of f. The subconvexity problem in the q-aspect is to replace the exponent 1/2 above by a strictly smaller one. In [KMV2], Theorem 1.1, we rayner memorialsWebtheory, but this paper is not concerned with this problem. Our object of study is the so-called Rankin–Selberg zeta function Z(s) = X1 n=1 c nn s; (1.4) which is the generating Dirichlet series for the sequence fc ng n 1. One can deﬁne the Rankin–Selberg zeta function in various degrees of generality; see, for rayner law grouphttp://www.math.keio.ac.jp/~kurihara/PANT2024/PANT2/PANTSlides/BingrongHuang.pdf simplink for pcWebThe 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 ... rayner low costWeb3 de fev. de 2024 · In this paper, we solve the Rankin–Selberg problem. That is, we break the. well known Rankin–Selberg’s bound on the e rror term of the second moment of … simpling cleaning