Number of proportions of Hecke eigenvalues in two newforms

초록

Let f(1) and f(2) be nonzero Hecke eigenforms on SL2(Z). For X > 0, let B(f(1), f(2), X) be the number of ratios of lambda(1)(p) to lambda(2)(p) for primes p <= X, where lambda(i)(p) denotes the Hecke eigenvalue of f(i) at p. In this paper, we prove that if f(1) is not a constant multiple of f(2), then B(f(1), f(2), X) >>(f1,f2) (log X)(1/15). (c) 2023 Elsevier Inc. All rights reserved.

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