On the rankin–selberg problem

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August undefined, 2024

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. … 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 …

[1109.1385] On the Rankin-Selberg problem in short intervals - arXiv

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 … 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 small square cloth men\u0027s handbags

On the Rankin-Selberg problem in families Request PDF

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. 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 … 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 ... highway 89 and post road

The Central value of the Rankin–Selberg L -Functions - Springer

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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 … 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 … highway 89 weather forecastWeb8 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 … highway 89 oregon

"WebThe 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 ... " - On the rankin–selberg problem

On the rankin–selberg problem

http://www.math.keio.ac.jp/~kurihara/PANT2024/PANT2/PANTSlides/BingrongHuang.pdf 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

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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. 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 …

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 ... 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 …

WebThe Rankin–Selberg problem, Hecke eigenvalues, second moment, L-functions, delta method. This workwas supported by the Taishan ScholarsProgramfor Young Expert of … 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 …

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

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 … small square dining table australiaWeb1 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. highway 8a nevadaWeb27 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. … small square dining room tablesWeb3 de fev. de 2024 · The Rankin–Selb erg problem, Hecke eigenvalues, second moment, L-functions, delta method. This work was supported by the Taishan Scholars Program … highway 8th 305 tamrin wisconsin 54822http://homepage.math.uiowa.edu/~yey/papers/gafa2002.pdf highway 89 minnesotaWeb12 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 … highway 89a azWebScience in China A: Mathematics. Pub Date: January 2008 DOI: 10.1007/s11425-007-0130-4 arXiv: arXiv:0805.1975 small square dining table living room