Abstract
For fixed positive integers k and N, there are only finitely many holomorphic eta quotients of weight k for the congruence subgroup \(\Gamma_{0}(N)\). In this article, we obtain a similar finiteness result for holomorphic generalized eta quotients of weight k on \(\Gamma_1(p)\) where k is a positive integer and p is a prime number. We also obtain a criterion for two holomorphic generalised eta quotients which represent the same one.
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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. The second author would like to thank KSoM, Kerala for providing financial support through institute fellowship.
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Agnihotri, R., Vaishya, L. A note on holomorphic generalized eta quotient. Acta Math. Hungar. 167, 393–403 (2022). https://doi.org/10.1007/s10474-022-01259-6
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DOI: https://doi.org/10.1007/s10474-022-01259-6