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January 18, 2026International Journal of Number Theory0 citations

Growth of Hecke eigenvalue ratios in newforms

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DKDuhyeon KimJRJaegwang Ryu

Key Points

  • To investigate the growth behavior of ratios of Hecke eigenvalues for various newforms.
  • Analyzed nonzero Hecke eigenforms under specific conditions.
  • Developed mathematical proofs regarding eigenvalue behaviors over primes.
  • Examined relationships between distinct Hecke eigenvalues.
  • Proven that non-constant Hecke eigenforms exhibit distinct growth in eigenvalue ratios.
  • Identified specific conditions that affect the ratio growth of eigenvalues.

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

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Cite This Study

Kim et al. (2026) studied this question.

synapsesocial.com/papers/696c774feb60fb80d13958fbhttps://doi.org/10.1142/s1793042126500594
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