Demonstrates the growth of eigenvalue ratios among non-constant Hecke eigenforms, indicating significant mathematical relationships.
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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Kim et al. (2026) studied this question.
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