Results 11 to 20 of about 11,043,146 (220)
Periods of automorphic forms over reductive subgroups [PDF]
Annales Scientifiques de l'Ecole Normale Supérieure, 2019 We present a regularization procedure of period integrals of automorphic forms on a group $G$ over an arbitrary reductive subgroup $G' \subset G$. As a consequence we obtain an explicit $G'(\mathbb{A})$-invariant functional on the space of automorphic ...
Michał Zydor
semanticscholar +1 more source
Application of automorphic forms to lattice problems
Journal of Mathematical Cryptology, 2022 In this article, we propose a new approach to the study of lattice problems used in cryptography. We specifically focus on module lattices of a fixed rank over some number field.
Düzlü Samed, Krämer Juliane
doaj +1 more source
The orbit method and analysis of automorphic forms [PDF]
Acta Mathematica, 2018 We develop the orbit method in a quantitative form, along the lines of microlocal analysis, and apply it to the analytic theory of automorphic forms.
Paul D. Nelson, Akshay Venkatesh
semanticscholar +1 more source
On triple correlation sums of Fourier coefficients of cusp forms
AIMS Mathematics, 2022 Let $ p $ be a prime. In this paper, we study the sum $ \sum\limits_{m\ge 1} \sum\limits_{n\ge 1} a_n \lambda_g(m)\lambda_{f}(m+pn) \,U{ \left( \frac{m}{X} \right) }V{ \left ( \frac{n}{H} \right)} $ for any newforms $ g\in \mathcal{B}_k(1 ...
Fei Hou , Bin Chen
doaj +1 more source
p-adic families of automorphic forms in the µ-ordinary setting [PDF]
American Journal of Mathematics, 2017 :We develop a theory of $p$-adic automorphic forms on unitary groups that allows $p$-adic interpolation in families and holds for all primes $p$ that do not ramify in the reflex field $E$ of the associated unitary Shimura variety.
E. Eischen, E. Mantovan
semanticscholar +1 more source
Automorphic Lie algebras and modular forms [PDF]
, 2020 We introduce and study hyperbolic versions of automorphic Lie algebras for the modular group $SL(2,\mathbb Z)$ acting naturally on the upper half-plane $\mathbb H^2$ and on the Lie algebra $\mathfrak g=sl(2, \mathbb C)$ by conjugation.
V. Knibbeler, S. Lombardo, A. Veselov
semanticscholar +1 more source
Differential equations in automorphic forms. [PDF]
, 2018 Physicists such as Green, Vanhove, et al show that differential equations involving automorphic forms govern the behavior of gravitons. One particular point of interest is solutions to $(\Delta-\lambda)u=E_{\alpha} E_{\beta}$ on an arithmetic quotient of
Kim Klinger-Logan
semanticscholar +1 more source
Reflective automorphic forms on lattices of squarefree level [PDF]
Transactions of the American Mathematical Society, 2018 We show that there are only finitely many nonconstant reflective automorphic forms $\Psi$ on even lattices of squarefree level splitting two hyperbolic planes and give a complete classification in the case where the zeros of $\Psi$ are simple and $\Psi ...
Moritz Dittmann
semanticscholar +1 more source
PERIODIC TWISTS OF $\operatorname{GL}_{3}$-AUTOMORPHIC FORMS
Forum of Mathematics, Sigma, 2020 We prove that sums of length about $q^{3/2}$ of Hecke eigenvalues of automorphic forms on $\operatorname{SL}_{3}(\mathbf{Z})$ do not correlate with $q$-periodic functions with bounded Fourier transform.
EMMANUEL KOWALSKI +3 more
doaj +1 more source
Pairings of automorphic distributions [PDF]
, 2011 We present a pairing of automorphic distributions that applies in situations where a Lie group acts with an open orbit on a product of generalized flag varieties.
Miller, Stephen D., Schmid, Wilfried
core +1 more source