On the arithmetic of special values of $L$-functions for certain abelian varieties with a rational isogeny

Autor:	Lecouturier, Emmanuel, Wang, Jun
Rok vydání:	2023
Předmět:	Mathematics - Number Theory
Druh dokumentu:	Working Paper
Popis:	Let $N$ and $p$ be primes $\geq 5$ such that $p \mid \mid N-1$. In this situation, Mazur defined and studied the $p$-Eisenstein quotient $\tilde{J}^{(p)}$ of $J_0(N)$. We prove a kind of modulo $p$ version of the Birch and Swinnerton-Dyer conjecture for the ``$p$-Eisenstein part'' of even quadratic twists of $\tilde{J}^{(p)}$. Our result is the analogue for even quadratic twists of a result of Mazur concerning odd quadratic twists. Comment: New version with corrections of our previous preprint
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.00643 Zobrazit plný text záznamu View this record from Arxiv