Rocky Mountain Journal of Mathematics

On the coefficients of triple product $L$-functions

Guangshi Lü and Ayyadurai Sankaranarayanan

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Abstract

In this paper, we investigate the average behavior of coefficients of the triple product $L$-function $L(f \otimes f \otimes f,s)$ attached to a primitive holomorphic cusp form $f(z)$ of weight~$k$ for the full modular group $SL(2, \Z )$. Here we call $f(z)$ a primitive cusp form if it is an eigenfunction of all Hecke operators simultaneously.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 2 (2017), 553-570.

Dates
First available in Project Euclid: 18 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1492502550

Digital Object Identifier
doi:10.1216/RMJ-2017-47-2-553

Mathematical Reviews number (MathSciNet)
MR3635374

Zentralblatt MATH identifier
06715761

Subjects
Primary: 11F30: Fourier coefficients of automorphic forms 11F66: Langlands $L$-functions; one variable Dirichlet series and functional equations

Keywords
Fourier coefficients of automorphic forms Dirichlet series triple product $L$-function Perron's formula

Citation

Lü, Guangshi; Sankaranarayanan, Ayyadurai. On the coefficients of triple product $L$-functions. Rocky Mountain J. Math. 47 (2017), no. 2, 553--570. doi:10.1216/RMJ-2017-47-2-553. https://projecteuclid.org/euclid.rmjm/1492502550


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