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Sign changes of certain arithmetical function at prime powers. (English) Zbl 07442487

Summary: We examine an arithmetical function defined by recursion relations on the sequence \(\{f(p^k)\}_{k\in\mathbb{N}}\) and obtain sufficient condition(s) for the sequence to change sign infinitely often. As an application we give criteria for infinitely many sign changes of Chebyshev polynomials and that of sequence formed by the Fourier coefficients of a cusp form.

MSC:

11A25 Arithmetic functions; related numbers; inversion formulas
11B83 Special sequences and polynomials
11F30 Fourier coefficients of automorphic forms
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