On the rankin–selberg problem

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August undefined, 2024

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 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

[2002.00591v4] On the Rankin--Selberg problem

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 … 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]. fly and cruise deals 2019

[2210.15095] On the Rankin-Selberg problem in families

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. http://homepage.math.uiowa.edu/~yey/papers/gafa2002.pdf Web23 de jan. de 2024 · Dr. P. Agarwal was born in Jaipur (India) on August 18, 1979. After completing his schooling, he earned his Master’s degree from Rajasthan University in 2000. In 2006, he earned his Ph. D. (Mathematics) at the MNIT in Jaipur, India, one of the highest-ranking universities in India. Dr. Agarwal has been actively involved in research as well … fly and cruise deals 2018

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

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 … 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 … fly and cruise caribbeanWeb5 de jun. de 2014 · The work in [10] did not consider the Markov case. A central problem in convex geometry is the computation of invariant, admissible, free groups. Introduction In [10], the authors constructed essentially canonical systems. ... contra-Selberg, sub-stochastically bounded function is contra-singular, if W ̄ > t then ̃I ∋ P. Since. fly and cruise holidays 2022

"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

ON SOME MEAN SQUARE ESTIMATES IN THE RANKIN-SELBERG PROBLEM

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 … 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

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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 … Web7 de set. de 2011 · In this paper, by assuming the generalized Lindel\"of hypothesis, we study the Rankin-Selberg problem in families of holomorphic modular forms. By using …

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 ... 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 …

Web3 de fev. de 2024 · arXivLabs: experimental projects with community collaborators. arXivLabs is a framework that allows collaborators to develop and share new arXiv … 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

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 …

WebPub Date: February 2024 arXiv: arXiv:2002.00591 Bibcode: 2024arXiv200200591H Keywords: Mathematics - Number Theory; E-Print: 28 pages. greenhorn mountain mapWebThe 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 ... fly and cruise packages 2017Web6 de abr. de 2024 · The second moment of the Fourier coefficients of triple product ... ... null fly and cruise hawaiiWebRankin-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. greenhorn onlineWebIvić 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 … fly and cruisesWeb10 de jan. de 2008 · Search 205,790,388 papers from all fields of science. Search. Sign In Create Free Account fly and cruise packages mediterraneanWebOn 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 fly and cruise packages miami