## Functiones et Approximatio Commentarii Mathematici

### Fourier coefficients of Hecke eigenforms

Ronald Evans

#### Abstract

We provide systematic evaluations, in terms of binary quadratic representations of $4p$, for the $p$-th Fourier coefficients of each member $f$ of an infinite class $\mathcal{C}$ of CM eigenforms. As an application, previously conjectured evaluations of three algebro-geometric character sums can now be formulated explicitly without reference to eigenforms. There are several non-CM newforms that appear to share some properties with the eigenforms in $\mathcal{C}$, and we pose some conjectures about their Fourier coefficients.

#### Article information

Source
Funct. Approx. Comment. Math., Volume 46, Number 2 (2012), 147-159.

Dates
First available in Project Euclid: 25 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.facm/1340628398

Digital Object Identifier
doi:10.7169/facm/2012.46.2.1

Mathematical Reviews number (MathSciNet)
MR2931662

Zentralblatt MATH identifier
1368.11038

#### Citation

Evans, Ronald. Fourier coefficients of Hecke eigenforms. Funct. Approx. Comment. Math. 46 (2012), no. 2, 147--159. doi:10.7169/facm/2012.46.2.1. https://projecteuclid.org/euclid.facm/1340628398

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