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Journal Article
Ramanujan-style congruences for prime level
2023
Overview
We establish Ramanujan-style congruences modulo certain primes
ℓ
between an Eisenstein series of weight
k
, prime level
p
and a cuspidal newform in the
ε
-eigenspace of the Atkin–Lehner operator inside the space of cusp forms of weight
k
for
Γ
0
(
p
)
. Under a mild assumption, this refines a result of Gaba–Popa. We use these congruences and recent work of Ciolan, Languasco and the third author on Euler–Kronecker constants, to quantify the non-divisibility of the Fourier coefficients involved by
ℓ
.
The degree of the number field generated by these coefficients we investigate using recent results on prime factors of shifted prime numbers.
Publisher
Springer Berlin Heidelberg,Springer Nature B.V
Subject
