On the rankin–selberg problem

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August undefined, 2024

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 …

[2210.15095] On the Rankin-Selberg problem in families

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. WebTHE SUBCONVEXITY PROBLEM FOR RANKIN-SELBERG L FUNCTIONS. 3 for 0, the implied constant depending on ε,s,gand the parameters at inﬁnity … how to increase hypocretin

(PDF) On the Rankin-Selberg problem: Higher power moments of …

WebRankin–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 ... 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 … 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 how to increase icloud storage capacity

SUBCONVEXITY FOR RANKIN-SELBERG L - University of Iowa

Transactions of the American Mathematical Society Series B

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 Category: Talk & Lecture. Speaker: Dr. LIN Yongxiao (Shandong University) Venue: Online. Tencent Meeting ID: 321-4296-7396. Webtheory, 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 how to increase icon size react iconsWeb4. 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. … how to increase icon size in bootstrap

"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 … " - On the rankin–selberg problem

On the rankin–selberg problem

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 …

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WebThe Rankin–Selberg problem, Hecke eigenvalues, second moment, L-functions, delta method. This workwas supported by the Taishan ScholarsProgramfor Young Expert of … Web26 de mai. de 2024 · The Rankin–Selberg problem is to improve the exponent 3/5. Although we have several methods to prove essentially the same bound as above (see e.g. Ivić [ 13 ]), the exponent 3/5 represents one of the longest standing records in analytic …

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]. Webthis is an important open problem. In this paper we establish such subcon-vexity estimates for special degree four L-functions, that is for Rankin Selberg L-functions of two degree two L-functions (one of which is fixed) doi:10.1006 jfan.2001.3783, available online at http: www.idealibrary.com on 419 0022-1236 01 ˚35.00

WebHá 1 dia · and last updated 6:14 PM, Apr 13, 2024. Sharan Rankin, a wheelchair user from Mesa, claims her accessibility needs were not met after waiting five hours at the airport waiting for a ride. "It's ... 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 …

WebRANKIN-SELBERG L FUNCTIONS IN THE LEVEL ASPECT E. KOWALSKI, P. MICHEL, AND J. VANDERKAM ... smallest quadratic non-residue problem was suggested to us by P. Sarnak. RANKIN-SELBERG LFUNCTIONS IN THE LEVEL ASPECT 3 Corollary 1.3. Let gbe a primitive cusp form as in Theorem 1.1 with D>1, k>2 an even

Web6 de abr. de 2024 · The second moment of the Fourier coefficients of triple product ... ... null how to increase icici cc limitWebIvić 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 … how to increase hypothyroid naturallyWeb14 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 … how to increase icloud storage from pcWebThe Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award honours the Canadian mathematician John Charles Fields.. The Fields Medal is regarded as one of the highest … how to increase icon font sizeWebIMRN 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 how to increase hz on lg monitorhttp://www.math.keio.ac.jp/~kurihara/PANT2024/PANT2/PANTSlides/BingrongHuang.pdf how to increase icon size in htmlWebOn 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. how to increase icon size in react