Euler-Kronecker constants of modular forms: beyond Dirichlet $L$-series

Autor:	Charlton, Steven, Medvedovsky, Anna, Moree, Pieter
Rok vydání:	2024
Předmět:	Mathematics - Number Theory
Druh dokumentu:	Working Paper
Popis:	The Euler-Kronecker constants related to congruences of Fourier coefficients of modular forms that have been computed so far, involve logarithmic derivatives of Dirichlet $L$-series as most complicated functions (to the best of our knowledge). However, generically the more complicated Artin $L$-series will make their appearance. Here we work out some simple examples involving an Artin $L$-series related to an ${\mathfrak S}_3$, respectively~${\mathfrak S}_4$ extension. These examples are related to a mod-2 congruence for $X_0(11)$, respectively a mod-59 congruence for $\Delta E_4$ conjectured by Serre and Swinnerton-Dyer and proved by Haberland. The latter example solves a problem posed by Ciolan, Languasco and the third author in 2023. Comment: 42 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.01803 Zobrazit plný text záznamu View this record from Arxiv