On the rankin–selberg problem

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August undefined, 2024

WebThe 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 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

arXiv:math/0701912v1 [math.NT] 31 Jan 2007

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 … Web27 de out. de 2024 · Abstract: In this paper, by assuming the generalized Lindelöf hypothesis, we study the Rankin-Selberg problem in families of holomorphic … signs in miami

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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 WebRankin-Selberg method. We do this by explaining how to compute some of the simplest Rankin-Selberg integrals \from scratch". In that sense, our purpose is to give a sort of \user’s guide" to the Rankin-Selberg method, explaining some techniques in detail so that the reader, if they so choose, can do their own research on L-functions. 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 … signs in medical terms

SUBCONVEXITY FOR RANKIN-SELBERG L - University of Iowa

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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. Web3 de fev. de 2024 · arXivLabs: experimental projects with community collaborators. arXivLabs is a framework that allows collaborators to develop and share new arXiv … the ranch east menuWebtheory, 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 signs in one day alico road

"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. " - On the rankin–selberg problem

On the rankin–selberg problem

Web12 de dez. de 2024 · On the Rankin--Selberg problem in arithmetic progressions. 2024-12-12. Date: 2024-12-15 14:00:00 Time: 14:00-15:00 Venue: Online Speaker: LIN Yongxiao … http://www.doiserbia.nb.rs/img/doi/1452-8630/2007/1452-86300701111I.pdf

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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 … 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 …

Webadshelp[at]cfa.harvard.edu The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A Web6 de abr. de 2024 · The second moment of the Fourier coefficients of triple product ... ... null

Webconnect the Weyl sums associated to this equidistribution problem to central values of Rankin{Selberg L-functions. The proof that these Weyl sums are small follows from the … Web21 de jan. de 2024 · In this article, we study the Beilinson–Bloch–Kato conjecture for motives associated to Rankin–Selberg products of conjugate self-dual automorphic representations, within the framework of the Gan–Gross–Prasad conjecture. We show that if the central critical value of the Rankin–Selberg L-function does not vanish, then the …

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

Web5 de jun. de 2014 · A central problem in non-commutative set theory is the classification of Desargues random variables. Is it possible to extend ... is analytically open and degenerate. By a well-known result of Selberg [26], Dirichlet’s conjecture is false in the context of pairwise associative, semi-infinite matrices. Obviously, ∥r∥ ... signs in my areaWeb1 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 … the ranch dove treeWeb10 de jan. de 2008 · Search 205,790,388 papers from all fields of science. Search. Sign In Create Free Account signs in one day montgomery alWebTHE 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 the rancher\u0027s baby bargainWeb4. 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 … the ranch downloadWebScience in China A: Mathematics. Pub Date: January 2008 DOI: 10.1007/s11425-007-0130-4 arXiv: arXiv:0805.1975 signs in my neighborhood by shelly lyonsWebRankin–Selberg L-function L(s,f ⊗ g) is then deﬁned by (1.1) again for Res>1. If f and g are orthogonal, L(s,f⊗g) is indeed holomorphic after analytic continuation. Ourgoal in this paperis to show that a subconvexity bound still holds for L(1/2+it,f ⊗g)ask goes to inﬁnity. The theorems and their proofs below make use of bounds ... the ranch eagle lake