Results 11 to 20 of about 112 (98)
Monodromy of four‐dimensional irreducible compatible systems of Q$\mathbb {Q}$
Bulletin of the London Mathematical Society, Volume 55, Issue 4, Page 1773-1790, August 2023., 2023 Abstract Let F$F$ be a totally real field and n⩽4$n\leqslant 4$ a natural number. We study the monodromy groups of any n$n$‐dimensional strictly compatible system {ρλ}λ$\lbrace \rho _\lambda \rbrace _\lambda$ of λ$\lambda$‐adic representations of F$F$ with distinct Hodge–Tate numbers such that ρλ0$\rho _{\lambda _0}$ is irreducible for some λ0$\lambda ...
Chun Yin Hui
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Mathematika, Volume 69, Issue 1, Page 250-285, January 2023., 2023 Abstract We introduce a class of multiplicative functions in which each function satisfies some statistic conditions, and then prove that the above functions are not correlated with finite degree polynomial nilsequences. Besides, we give two applications of this result. One is that the twisting of coefficients of automorphic L‐function on GLm(m⩾2)$GL_m
Xiaoguang He, Mengdi Wang
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The Arithmetic of the Fourier Coefficients of Automorphic Forms
, 2023 PhD thesis, 141 pages.
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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
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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 +4 more
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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
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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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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
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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
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