Geodesic
Sign changes of certain arithmetical function at prime powers
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1221-1228
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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.
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.
DOI : 10.21136/CMJ.2021.0398-20
Classification : 11A25, 11B39, 11F30, 11M38
Keywords: arithmetic function; Dirichlet series; Chebyschev polynomial; modular form 
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Agnihotri, Rishabh; Chakraborty, Kalyan. Sign changes of certain arithmetical function at prime powers. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1221-1228. doi: 10.21136/CMJ.2021.0398-20

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