Experimental Mathematics

Numerical calculation of twisted adjoint $L$-values attached to modular forms

Yoshio Hiraoka

Abstract

Doi, Hida, and Ishii have shown that the values of twisted adjoint $L$-functions $L(1,\Ad(f)\otimes\chi)$ attached to modular forms $f$ are closely connected with discriminants of Hecke fields. Goto has given a numerical example of this $L$-value for an elliptic cusp form $f$ of level $1$ and weight $20$. We shall show a method to calculate the $L$-values, which is more effective than Goto's, and give new numerical examples.

Article information

Source
Experiment. Math., Volume 9, Issue 1 (2000), 67-73.

Dates
First available in Project Euclid: 5 March 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1046889591

Mathematical Reviews number (MathSciNet)
MR1758800

Zentralblatt MATH identifier
0972.11042

Subjects
Primary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
Secondary: 11F41: Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]

Citation

Hiraoka, Yoshio. Numerical calculation of twisted adjoint $L$-values attached to modular forms. Experiment. Math. 9 (2000), no. 1, 67--73. https://projecteuclid.org/euclid.em/1046889591


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