TY - JOUR

T1 - Apéry-like numbers and families of newforms with complex multiplication

AU - Gomez, Alexis

AU - McCarthy, Dermot

AU - Young, Dylan

N1 - Funding Information:
The second author is supported by a grant from the Simons Foundation (353329, Dermot McCarthy).
Publisher Copyright:
© 2018, SpringerNature.

PY - 2019/3/1

Y1 - 2019/3/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85058842084&partnerID=8YFLogxK

U2 - 10.1007/s40993-018-0145-7

DO - 10.1007/s40993-018-0145-7

M3 - Article

AN - SCOPUS:85058842084

VL - 5

JO - Research in Number Theory

JF - Research in Number Theory

SN - 2363-9555

IS - 1

M1 - 5

ER -