Abstract
Quite recently, Tang extensively studied the vanishing coefficients in arithmetic progressions of the following three types of infinite q-products:
where \(j, k, s, u\in {\mathbb {Z}}^{+}\), \(r\ge 2\), and \(n_0\) is an integer (possibly negative or zero) depending on j, k, r, s, u. In this paper, we further explore the vanishing coefficients for arithmetic progressions modulo 13, 17, 19 and 29 in the above three infinite products. For example, we prove that
where \(\alpha \ge 1\), \(\gcd (r,t)=1\) with \(r \in \{13,17,19,29\}\).
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Acknowledgements
The first author’s research was financed by the KSTePS (Ref. No.: DST/KSTePS/Ph.D.Fellowship/MAT-01:2021-22/1195), Government of Karnataka. The authors thank the anonymous referees for their diligent review and insightful comments, which improved the quality of the manuscript.
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Channabasavayya, Dasappa, R. Vanishing coefficients in arithmetic progressions of some infinite products with modulo 13, 17, 19 and 29. J Anal (2024). https://doi.org/10.1007/s41478-024-00784-7
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DOI: https://doi.org/10.1007/s41478-024-00784-7