Results 31 to 40 of about 260 (137)
Character sum, reciprocity, and Voronoi formula
Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3797-3823, December 2025.Abstract We prove a novel four‐variable character sum identity that serves as a twisted, non‐Archimedean analog of Weber's integrals for Bessel functions. Using this identity and ideas from Venkatesh's thesis, we provide a short spectral proof of the Voronoi formulae for classical modular forms with character twists.
Chung‐Hang Kwan, Wing Hong Leung
wiley +1 more source
Soft bounds for local triple products and the subconvexity‐QUE implication for GL2$\mathrm{GL}_2$
Mathematika, Volume 71, Issue 4, October 2025.Abstract We give a soft proof of a uniform upper bound for the local factors in the triple product formula, sufficient for deducing effective and general forms of quantum unique ergodicity (QUE) from subconvexity.
Paul D. Nelson
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Correlations of the squares of the Riemann zeta function on the critical line
Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.Abstract We compute the average of a product of two shifted squares of the Riemann zeta function on the critical line with shifts up to size T3/2−ε$T^{3/2-\varepsilon }$. We give an explicit expression for such an average and derive an approximate spectral expansion for the error term similar to Motohashi's.
Valeriya Kovaleva
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Lp$L^p$‐norm bounds for automorphic forms via spectral reciprocity
Proceedings of the London Mathematical Society, Volume 130, Issue 6, June 2025.Abstract Let g$g$ be a Hecke–Maaß cusp form on the modular surface SL2(Z)∖H$\operatorname{SL}_2(\mathbb {Z}) \backslash \mathbb {H}$, namely an L2$L^2$‐normalised non‐constant Laplacian eigenfunction on SL2(Z)∖H$\operatorname{SL}_2(\mathbb {Z}) \backslash \mathbb {H}$ that is additionally a joint eigenfunction of every Hecke operator. We prove the L4$L^
Peter Humphries, Rizwanur Khan
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Automorphic Forms and Arithmetic
, 2017 The workshop brought together leading experts and young researchers at the interface of automorphic forms and analytic number theory to disseminate, discuss and develop important recent methods and results.
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Bounds on Fourier coefficients and global sup‐norms for Siegel cusp forms of degree 2
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract Let F$F$ be an L2$L^2$‐normalized Siegel cusp form for Sp4(Z)${\rm Sp}_4({\mathbb {Z}})$ of weight k$k$ that is a Hecke eigenform and not a Saito–Kurokawa lift. Assuming the generalized Riemann hypothesis, we prove that its Fourier coefficients satisfy the bound |a(F,S)|≪εk1/4+ε(4π)kΓ(k)c(S)−12det(S)k−12+ε$|a(F,S)| \ll _\epsilon \frac{k^{1/4 ...
Félicien Comtat +2 more
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Moments of symmetric square L$L$‐functions on GL(3)${\rm GL}(3)$
Proceedings of the London Mathematical Society, Volume 130, Issue 3, March 2025.Abstract We give an asymptotic formula with power saving error term for the twisted first moment of symmetric square L$L$‐functions on GL(3)${\rm GL}(3)$ in the level aspect. As applications, we obtain nonvanishing results as well as lower bounds of the expected order of magnitude for all even moments, supporting the random matrix model for a unitary ...
Valentin Blomer, Félicien Comtat
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Fourier coefficients for automorphic forms on quasisplit classical groups
, 2014 To James Cogdell, on the occasion of his 60th ...
Jiang, Dihua, Liu, Baiying
openaire +2 more sources
L${L}$‐functions of Kloosterman sheaves
Proceedings of the London Mathematical Society, Volume 129, Issue 5, November 2024.Abstract In this article, we study a family of motives Mn+1k$\mathrm{M}_{n+1}^k$ associated with the symmetric power of Kloosterman sheaves constructed by Fresán, Sabbah, and Yu. They demonstrated that for n=1$n=1$, the L$L$‐functions of M2k$\mathrm{M}_{2}^k$ extend meromorphically to C$\mathbb {C}$ and satisfy the functional equations conjectured by ...
Yichen Qin
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A large sieve inequality of elliott-montgomery-vaughan type for automorphic forms and two applications [PDF]
, 2008 In this paper, we establish a large sieve inequality of Elliott-Montgomery-Vaughan type for Fourier coefficients of newforms. As applications, we give a significant improvement on the principal result of Duke and Kowalski on Linnik's problem for modular ...
Lau, YK, Wu, J
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