Czechoslovak Mathematical Journal, Vol. 71, No. 4, pp. 1221-1228, 2021


Sign changes of certain arithmetical function at prime powers

Rishabh Agnihotri, Kalyan Chakraborty

Received September 14, 2020.   Published online April 23, 2021.

Abstract:  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.
Keywords:  arithmetic function; Dirichlet series; Chebyschev polynomial; modular form
Classification MSC:  11A25, 11M38, 11B39, 11F30


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Affiliations:   Rishabh Agnihotri (corresponding author), Harish-Chandra Research Institute, Homi Bhabha National Institute, Chhatnag Road, Jhunsi, Prayagraj 211019, India, e-mail: rishabhagnihotri663@gmail.com, rishabhagnihotri@hri.res.in; Kalyan Chakraborty, KSCSTE-Kerala School of Mathematics, Kunnamangalam PO, Kozhikode, Kerala 673571, India, Harish-Chandra Research Institute, Homi Bhabha National Institute, Chhatnag Road, Jhunsi, Prayagraj 211019, India, e-mail: kalychak@ksom.res.in, kalyan@hri.res.in


 
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