Examples of Shimura correspondence for level p^2 and real quadratic twists

Abstract

We give examples of Shimura correspondence for rational modular forms f of weight 2 and level p^2, for primes p<=19, computed as an application of a method we introduced in \cite{Pacetti-Tornaria}. Furthermore, we verify in this examples a conjectural formula for the central values L(f,-pd,1) and, in case p = 3 (mod 4), a formula for the central values L(f,d,1) corresponding to the real quadratic twists of f.

21 pages, submitted to "Elliptic curves and random matrix theory."

Cited by in corpus (3)

• Shimura correspondence for level $p^2$ and the central values of $L$-series II
• Nonvanishing of twists of $L$-functions attached to Hilbert modular forms
• Computing central values of $L$-functions