Taiwanese Journal of Mathematics

$L$-series for Vector-valued Modular Forms

Byungchan Kim and Subong Lim

Full-text: Open access

Abstract

Motivated by the recent works of Bringmann, Guerzhoy, Kent, and Ono [4] and Bringmann, Fricke, and Kent [3], we introduce $L$-series for vector-valued weakly holomorphic cusp forms, and mock modular period polynomials for vector-valued harmonic weak Maass forms. In particular, we will discuss an integral representation of this new $L$-series and the limiting behavior of special values. Moreover, we also give relations between mock modular periods and $L$-series for vector-valued harmonic weak Maass forms.

Article information

Source
Taiwanese J. Math., Volume 20, Number 4 (2016), 705-722.

Dates
First available in Project Euclid: 1 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1498874486

Digital Object Identifier
doi:10.11650/tjm.20.2016.5976

Mathematical Reviews number (MathSciNet)
MR3535669

Zentralblatt MATH identifier
1366.11073

Subjects
Primary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols

Keywords
$L$-series vector-valued modular forms vector-valued harmonic weak Maass forms period polynomials

Citation

Kim, Byungchan; Lim, Subong. $L$-series for Vector-valued Modular Forms. Taiwanese J. Math. 20 (2016), no. 4, 705--722. doi:10.11650/tjm.20.2016.5976. https://projecteuclid.org/euclid.twjm/1498874486


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