Results 31 to 40 of about 167,541,873 (127)
Joint distribution of Hecke eigenforms on H3$ \mathbb {H}^3$
Mathematische Nachrichten, Volume 299, Issue 3, Page 661-674, March 2026.Abstract We prove a joint value equidistribution statement for Hecke–Maaß cusp forms on the hyperbolic three‐space H3$\mathbb {H}^3$. This supports the conjectural statistical independence of orthogonal cusp forms.
Didier Lesesvre +2 more
wiley +1 more source
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
Automorphic Forms and Arithmetic [PDF]
, 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.
core +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
wiley +1 more source
Notes on automorphic functions: an entire automorphic form of positive dimension is zero
, 1967 Several new proofs are given of the fact that an entire automorphic form of positive dimension is zero. The first proof is modeled on the method used by Hecke to estimate the Fourier coefficients of cusp forms of nega tive dimension.
Knopp, Marvin I.
core +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
wiley +1 more source
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
wiley +1 more source
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$L^
Peter Humphries, Rizwanur Khan
wiley +1 more source
Bounds on Fourier coefficients and global sup‐norms for Siegel cusp forms of degree 2
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract Let F$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
Level-Raising for GSp(4) [PDF]
, 2006 This thesis provides congruences between unstable and stable automorphic forms for the symplectic similitude group $GSp(4)$. More precisely, we raise the level of certain CAP representations $Pi$ of Saito-Kurokawa type, arising from classical modular ...
Sorensen, Claus Mazanti
core +1 more source