Non-critical equivariant L-values of modular abelian varieties

Abstract

We prove an equivariant version of Beilinson's conjecture on non-critical $L$-values of strongly modular abelian varieties over number fields. As an application, we prove a weak version of Zagier's conjecture on $L(E,2)$ and Deninger's conjecture on $L(E,3)$ for non-CM strongly modular $\mathbf{Q}$-curves.

18 pages

References in corpus (2)

• On the Brauer class of Modular Endomorphism Algebras
• Modular abelian varieties over number fields