The 2-adic valuations of the algebraic central $L$-values for quadratic twists of weight 2 newforms

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Adachi, Taiga, Nomoto, Keiichiro, Shii, Ryota
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866915539860848640
author Adachi, Taiga
Nomoto, Keiichiro
Shii, Ryota
author_facet Adachi, Taiga
Nomoto, Keiichiro
Shii, Ryota
contents Let $f$ be a normalized newform of weight 2 on $Γ_0(N)$ whose coefficients lie in $\mathbb{Q}$ and let $χ_M$ be a primitive quadratic Dirichlet character with conductor $M$. In this paper, under mild assumptions on $M$, we give a sharp lower bound of the 2-adic valuation of the algebraic central $L$-value $L(f, χ_M, 1)$ and evaluate the 2-adic valuation for an infinite number of $M$.
format Preprint
id arxiv_https___arxiv_org_abs_2403_11474
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The 2-adic valuations of the algebraic central $L$-values for quadratic twists of weight 2 newforms
Adachi, Taiga
Nomoto, Keiichiro
Shii, Ryota
Number Theory
Let $f$ be a normalized newform of weight 2 on $Γ_0(N)$ whose coefficients lie in $\mathbb{Q}$ and let $χ_M$ be a primitive quadratic Dirichlet character with conductor $M$. In this paper, under mild assumptions on $M$, we give a sharp lower bound of the 2-adic valuation of the algebraic central $L$-value $L(f, χ_M, 1)$ and evaluate the 2-adic valuation for an infinite number of $M$.
title The 2-adic valuations of the algebraic central $L$-values for quadratic twists of weight 2 newforms
topic Number Theory
url https://arxiv.org/abs/2403.11474