Functiones et Approximatio Commentarii Mathematici

Non-vanishing of derivatives of certain modular $L$-functions

Narasimha Kumar

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Abstract

This paper is to show a non-vanishing property of the derivatives of certain class of $L$-functions. We study the non-vanishing and transcendence of special values of $L$-functions and their derivatives, attached to (cuspidal) Siegel-Hecke eigenforms of genus $2$, quadratic twists of classical Hecke eigenforms, and half-integral weight modular forms.

Article information

Source
Funct. Approx. Comment. Math., Volume 51, Number 1 (2014), 121-132.

Dates
First available in Project Euclid: 24 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.facm/1411564618

Digital Object Identifier
doi:10.7169/facm/2014.51.1.6

Mathematical Reviews number (MathSciNet)
MR3263072

Zentralblatt MATH identifier
1359.11054

Subjects
Primary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols 11J81: Transcendence (general theory)
Secondary: 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms 11F11: Holomorphic modular forms of integral weight 11F37: Forms of half-integer weight; nonholomorphic modular forms

Keywords
Siegel modular forms twists of cusp forms half-integral weight modular forms $L$-functions non-vanishing special values transcendence

Citation

Kumar, Narasimha. Non-vanishing of derivatives of certain modular $L$-functions. Funct. Approx. Comment. Math. 51 (2014), no. 1, 121--132. doi:10.7169/facm/2014.51.1.6. https://projecteuclid.org/euclid.facm/1411564618


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