Results 21 to 30 of about 6,212 (114)
One‐level densities in families of Grössencharakters associated to CM elliptic curves
Mathematika, Volume 72, Issue 1, January 2026.Abstract We study the low‐lying zeros of a family of L$L$‐functions attached to the complex multiplication elliptic curve Ed:y2=x3−dx$E_d \;:\; y^2 = x^3 - dx$, for each odd and square‐free integer d$d$. Specifically, upon writing the L$L$‐function of Ed$E_d$ as L(s−12,ξd)$L(s-\frac{1}{2}, \xi _d)$ for the appropriate Grössencharakter ξd$\xi _d$ of ...
Chantal David, Lucile Devin, Ezra Waxman
wiley +1 more source
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
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Fourier coefficients of automorphic forms and integrable discrete series
Journal of Functional Analysis, 2016 Let $G$ be the group of $\mathbb R$--points of a semisimple algebraic group $\mathcal G$ defined over $\mathbb Q$. Assume that $G$ is connected and noncompact. We study Fourier coefficients of Poincar\' e series attached to matrix coefficients of integrable discrete series.
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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
wiley +1 more source
p-adic Eisenstein series and L-functions of certain cusp forms on definite unitary groups
, 2014 We construct p-adic families of Klingen Eisenstein series and L-functions for cuspforms (not necessarily ordinary) unramified at an odd prime p on definite unitary groups of signature (r, 0) (for any positive integer r) for a quadratic imaginary field ...
Eischen, Ellen, Wan, Xin
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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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The Igusa modular forms and ``the simplest'' Lorentzian Kac--Moody algebras
, 1996 We find automorphic corrections for the Lorentzian Kac--Moody algebras with the simplest generalized Cartan matrices of rank 3: A_{1,0} = 2 0 -1 0 2 -2 -1 -2 2 and A_{1,I} = 2 -2 -1 -2 2 -1 -1 -1 2 For A_{1,0} this correction is given
Gritsenko, Valeri A. +1 more
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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$L^
Peter Humphries, Rizwanur Khan
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Bounds on Fourier coefficients and global sup‐norms for Siegel cusp forms of degree 2
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract Let F$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
wiley +1 more source
Fourier coefficients of automorphic forms, character variety orbits, and small representations
Journal of Number Theory, 2012 We consider the Fourier expansions of automorphic forms on general Lie groups, with a particular emphasis on exceptional groups. After describing some principles underlying known results on GL(n), Sp(4), and G_2, we perform an analysis of the expansions on split real forms of E_6 and E_7 where simplifications take place for automorphic realizations of ...
Miller, Stephen D., Sahi, Siddhartha
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