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Sign changes of certain arithmetical function at prime powers

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Abstract

We examine an arithmetical function defined by recursion relations on the sequence {f(pk)}k∈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.

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Acknowledgements

The authors are indebted to Professor B. Ramakrishnan for his encouragement and for many fruitful suggestions. The authors are grateful to anonymous referee for his/her valuable suggestions and remarks which improved the exposition of the paper. The authors acknowledge Harish-Chandra Research Institute for fantastic facilities and for the serene ambience that it facilitates.

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Authors and Affiliations

  1. Harish-Chandra Research Institute, Homi Bhabha National Institute, Chhatnag Road, Jhunsi, Prayagraj, 211019, India

    Rishabh Agnihotri & Kalyan Chakraborty

  2. KSCSTE-Kerala School of Mathematics, Kunnamangalam PO, Kozhikode, Kerala, 673571, India

    Kalyan Chakraborty

Authors
  1. Rishabh Agnihotri
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  2. Kalyan Chakraborty
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Correspondence to Rishabh Agnihotri.

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Agnihotri, R., Chakraborty, K. Sign changes of certain arithmetical function at prime powers. Czech Math J 71, 1221–1228 (2021). https://doi.org/10.21136/CMJ.2021.0398-20

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  • DOI: https://doi.org/10.21136/CMJ.2021.0398-20

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