Growth of Hecke eigenvalue ratios in newforms

Let [Formula: see text] be nonzero Hecke eigenforms on [Formula: see text]. For [Formula: see text], let [Formula: see text] be the number of ratios of [Formula: see text] for primes [Formula: see text], where [Formula: see text] denotes the Hecke eigenvalue of [Formula: see text] at [Formula: see text]. In this paper, we prove that if [Formula: see text] is not a constant multiple of [Formula: see text] for distinct [Formula: see text], then [Formula: see text]

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Publication Details

Journal
International Journal of Number Theory
Published
2026-01-16
DOI
https://doi.org/10.1142/s1793042126500594
Primary Topic
Analytic Number Theory Research
Type
article
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article

Growth of Hecke eigenvalue ratios in newforms

Jaegwang Ryu, Duhyeon Kim
International Journal of Number Theory
Analytic Number Theory Research
article

Growth of Hecke eigenvalue ratios in newforms

Jaegwang Ryu, Duhyeon Kim
article en

Abstract

Let [Formula: see text] be nonzero Hecke eigenforms on [Formula: see text]. For [Formula: see text], let [Formula: see text] be the number of ratios of [Formula: see text] for primes [Formula: see text], where [Formula: see text] denotes the Hecke eigenvalue of [Formula: see text] at [Formula: see text]. In this paper, we prove that if [Formula: see text] is not a constant multiple of [Formula: see text] for distinct [Formula: see text], then [Formula: see text]

International Journal of Number Theory
Korea University (KR)
Openalex Percentile: Top 82%
Analytic Number Theory Research
DOISourceOpenAlex
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Growth of Hecke eigenvalue ratios in newforms — Jaegwang Ryu, Duhyeon Kim · International Journal of Number Theory (2026) | TGRS Research Map | TGRS