On the rankin-selberg problem

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August undefined, 2024

WebTHE RANKIN-SELBERG PROBLEM Aleksandar Ivic An overview of the classical Rankin-Selberg problem involving the asymp-totic formula for sums of coefficients of … Web27 de out. de 2024 · On the Rankin-Selberg problem in families. Jiseong Kim. In 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-average bound, we also study the Rankin-Selberg problem in families of Hecke-Maass cusp forms. …

[2002.00591] On the Rankin--Selberg problem - arXiv.org

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. Web8 de jan. de 2009 · Let f be a Maass form for SL $$(3, {\\mathbb{Z}})$$ which is fixed and u j be an orthonormal basis of even Maass forms for SL $$(2, {\\mathbb{Z}})$$ , we prove an asymptotic formula for the average of the product of the Rankin–Selberg L-function of f and u j and the L-function of u j at the central value 1/2. This implies simultaneous … ontstoringsfilter audio

The second moment of the Fourier coefficients of triple product ...

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 … Web13 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 … 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]. ontstoppingsmachine huren

On the fourth moment in the Rankin-Selberg problem - Springer

On Riesz means of the coefficients of the Rankin–Selberg series

Web4. A shifted convolution problem 29 5. Expanding the c-sum 34 6. Heegner points on Shimura curves 44 7. Appendix: Bounds for Bessel functions 47 References 50 1. Introduction In this paper, we pursue the program—initiated in [KMV02] and continued in [M04a]—of solving the subconvexity problem for Rankin–Selberg L-functions in the … iotc 0370 chipWebIMRN 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 ontstrand

"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. " - On the rankin-selberg problem

On the rankin-selberg problem

On a Rankin-Selberg -Function over Different Fields - Semantic …

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 WebTHE 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

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WebPub Date: February 2024 arXiv: arXiv:2002.00591 Bibcode: 2024arXiv200200591H Keywords: Mathematics - Number Theory; E-Print: 28 pages. 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 …

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 ... Web3 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 …

Web27 de out. de 2024 · On the Rankin-Selberg problem in families. In this paper, by assuming the generalized Lindelöf hypothesis, we study the Rankin-Selberg … http://www.math.keio.ac.jp/~kurihara/PANT2024/PANT2/PANTSlides/BingrongHuang.pdf

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 …

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; ontstorenWeb3 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% … ontstoppingsservice 24/7Web14 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 … iot business opportunities ppthttp://homepage.math.uiowa.edu/~yey/papers/gafa2002.pdf ontstoppingsputWeb7 de set. de 2011 · Comments: 12 pages: Subjects: Number Theory (math.NT) MSC classes: : 11N37, 44A15, 26A12: Journal reference: Moscow Journal of Combinatorics … ontstoppingsmachineWeb1 de jul. de 2004 · In this paper we study the subconvexity problem for the Rankin-Selberg L-function and triple product L-function, allowing joint ramifications and conductor dropping range. We first extend … Expand. 1. PDF. Save. Alert. The subconvexity problem for Rankin–Selberg L-functions and equidistribution of Heegner points. II. ontstoppingsserviceWebThe Rankin-Selberg problem, Vorono¨ı type formula, Selberg class, mean square estimates. Typeset by AMS-TEX 1. 2 Aleksandar Ivi´c The constant C(> 0) in (1) may be written down explicitly (see e.g., [7]), and cn is the convolution function deﬁned by iotc-0610