On the Equality Case of the Ramanujan Conjecture for Hilbert Modular Forms

Authors

Liubomir Chiriac, Portland State UniversityFollow

Published In

International Journal of Number Theory

Document Type

Post-Print

Publication Date

11-1-2019

Subjects

Number theory, Modular forms, Hilbert modular surfaces, Eigenvalues

Abstract

The generalized Ramanujan Conjecture for cuspidal unitary automorphic representations π on GL(2) asserts that |av(π)| ≤ 2. We prove that this inequality is strict if π is generated by a CM Hilbert modular form of parallel weight two and v is a finite place of degree one. Equivalently, the Satake parameters of πv are necessarily distinct. We also give examples where the equality case does occur for primes of degree two.

Description

Electronic version of an article published as:

Chiriac, L. (2019). On the equality case of the Ramanujan Conjecture for Hilbert modular forms. International Journal of Number Theory, 1-8.

Copyright 2019 World Scientific Publishing Company

Locate the Document

http://doi.org/10.1142/S179304211950115X

DOI

10.1142/S179304211950115X

Persistent Identifier

https://archives.pdx.edu/ds/psu/30928

Citation Details

Chiriac, L. (2019). On the equality case of the Ramanujan Conjecture for Hilbert modular forms. International Journal of Number Theory, 1-8.