Apéry-like numbers and families of newforms with complex multiplication

Alexis Gomez, Dermot McCarthy, Dylan Young

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Using Hecke characters, we construct two infinite families of newforms with complex multiplication, one by Q(-3) and the other by Q(-2). The values of the p-th Fourier coefficients of all the forms in each family can be described by a single formula, which we provide explicitly. This allows us to establish a formula relating the p-th Fourier coefficients of forms of different weights, within each family. We then prove congruence relations between the p-th Fourier coefficients of these newforms at all odd weights and values coming from two of Zagier’s sporadic Apéry-like sequences.

Original languageEnglish
Article number5
JournalResearch in Number Theory
Volume5
Issue number1
DOIs
StatePublished - Mar 1 2019

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