Results 81 to 90 of about 11,043,146 (220)

Counting integral points on symmetric varieties with applications to arithmetic statistics

Proceedings of the London Mathematical Society, Volume 130, Issue 4, April 2025.
Abstract In this article, we combine Bhargava's geometry‐of‐numbers methods with the dynamical point‐counting methods of Eskin–McMullen and Benoist–Oh to develop a new technique for counting integral points on symmetric varieties lying within fundamental domains for coregular representations.
Arul Shankar, Artane Siad, Ashvin A. Swaminathan   +2 more
wiley   +1 more source

Stable Automorphic Forms for Semisimple Groups

, 2019
In this paper, we introduce the concept of stable automorphic forms for semisimple algebraic groups and use the stability of automorphic forms to study infinite dimensional arithmetic quotients.Comment: 27 ...
Yang, Jae-Hyun
core  

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, Jolanta Marzec‐Ballesteros, Abhishek Saha   +2 more
wiley   +1 more source

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
wiley   +1 more source

THE INTEGRAL OPERATOR OF PROJECTION AND POINCARE SERIES FOR HOLOMORPHIC (Q; Ρ ) − FORMS

Вестник Кемеровского государственного университета, 2013
The paper addresses the spaces of multiplicate integrable automorphic forms on the plane domain D and on the compact Riemann surface D/G; where the group G is isomorphic to Fuchsian group of the first kind.
O. A. Sergeeva
doaj  

Modular forms for three-loop banana integrals

Journal of High Energy Physics
We study periods of multi-parameter families of K3 surfaces, which are relevant to compute the maximal cuts of certain classes of Feynman integrals. We focus on their automorphic properties, and we show that generically the periods define orthogonal ...
Claude Duhr
doaj   +1 more source

Unitary Friedberg–Jacquet periods and anticyclotomic p-adic L-functions

Forum of Mathematics, Sigma
We extend the construction of the p-adic L-function interpolating unitary Friedberg–Jacquet periods in previous work of the author to include the p-adic variation of Maass–Shimura differential operators.
Andrew Graham
doaj   +1 more source

Quadratic Forms and Automorphic Forms [PDF]

, 2013
These notes give a friendly four-part introduction to various aspects of the arithmetic and analytic theories of quadratic forms, aimed at a graduate-level audience. The main themes discussed are: geometry and local-global methods, theta functions and Siegel’s theorem, Clifford algebras and spin groups, and adelic theta liftings via the Weil ...
openaire   +1 more source

On vertex‐transitive graphs with a unique hamiltonian cycle

Journal of Graph Theory, Volume 108, Issue 1, Page 65-99, January 2025.
Abstract A graph is said to be uniquely hamiltonian if it has a unique hamiltonian cycle. For a natural extension of this concept to infinite graphs, we find all uniquely hamiltonian vertex‐transitive graphs with finitely many ends, and also discuss some examples with infinitely many ends.
Babak Miraftab, Dave Witte Morris
wiley   +1 more source

Smith theory and cyclic base change functoriality

Forum of Mathematics, Pi
Lafforgue and Genestier-Lafforgue have constructed the global and (semisimplified) local Langlands correspondences for arbitrary reductive groups over function fields.
Tony Feng
doaj   +1 more source