Results 21 to 30 of about 260 (137)

Fourier coefficients of minimal and next-to-minimal automorphic representations of simply-laced groups

, 2022
In this paper we analyze Fourier coefficients of automorphic forms on adelic split simply-laced reductive groups $G(\mathbb{A})$. Let $\pi$ be a minimal or next-to-minimal automorphic representation of $G(\mathbb{A})$.
Gourevitch, Dmitry,, Kleinschmidt, Axel, Sahi, Siddhartha, Gustafsson, H., Kleinschmidt, A., Gustafsson, Henrik, Sahi, S., Persson, Daniel, Gourevitch, D., Persson, D., Sahi, Siddhartha,, Kleinschmidt, Axel,, Persson, Daniel,, Gourevitch, Dmitry, Gustafsson, Henrik,   +14 more
core   +1 more source

Symplectic Automorphic Forms and Kloosterman Sums [PDF]

, 2021
In this thesis, we study automorphic forms on the rank 2 symplectic group Sp(4), in the context of analytic number theory. While much of the abstract theory is described in Langlands’ theory, one needs more explicit formulae for applications in analytic ...
Man, Siu Hang
core  

Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the String‐Theoretical Swampland Programme

Fortschritte der Physik, Volume 74, Issue 4, April 2026.
Abstract String theory has strong implications for cosmology, implying the absence of a cosmological constant, ruling out single‐field slow‐roll inflation, and that black holes decay. The origins of these statements are elucidated within the string‐theoretical swampland programme.
Kay Lehnert
wiley   +1 more source

Tessellation Groups, Harmonic Analysis on Non‐Compact Symmetric Spaces and the Heat Kernel in View of Cartan Convolutional Neural networks

Fortschritte der Physik, Volume 74, Issue 4, April 2026.
ABSTRACT In this paper, we continue the development of the Cartan neural networks programme, launched with three previous publications, by focusing on some mathematical foundational aspects that we deem necessary for our next steps forward. The mathematical and conceptual results are diverse and span various mathematical fields, but the inspiring ...
Pietro Fré, Federico Milanesio, Marcelo Oyarzo, Matteo Santoro, Mario Trigiante   +4 more
wiley   +1 more source

Moments of L$L$‐functions via a relative trace formula

Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.
Abstract We prove an asymptotic formula for the second moment of the GL(n)×GL(n−1)$\mathrm{GL}(n)\times \mathrm{GL}(n-1)$ Rankin–Selberg central L$L$‐values L(1/2,Π⊗π)$L(1/2,\Pi \otimes \pi)$, where π$\pi$ is a fixed cuspidal representation of GL(n−1)$\mathrm{GL}(n-1)$ that is tempered and unramified at every place, while Π$\Pi$ varies over a family of
Subhajit Jana, Ramon Nunes
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

Rational points in a family of conics over F2(t)$\mathbb {F}_2(t)$

Mathematische Nachrichten, Volume 299, Issue 3, Page 496-513, March 2026.
Abstract Serre famously showed that almost all plane conics over Q$\mathbb {Q}$ have no rational point. We investigate versions of this over global function fields, focusing on a specific family of conics over F2(t)$\mathbb {F}_2(t)$ which illustrates new behavior.
Daniel Loughran, Judith Ortmann
wiley   +1 more source

Fourier expansions of vector-valued automorphic functions with non-unitary twists

, 2023
We provide Fourier expansions of vector-valued eigenfunctions of the hyperbolic Laplacian that are twist-periodic in a horocycle direction. The twist may be given by any endomorphism of a finite-dimensional vector space; no assumptions on invertibility ...
Fedosova, Ksenia, Rowlett, Julie, Rowlett, Julie,, Pohl, Anke   +3 more
core   +1 more source

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, Luca Marchesini, Nicole Raulf   +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