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On the q-Exponents of Generalized Modular Functions

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Abstract

We consider two problems concerning oscillations of the q-exponents of generalized modular functions. First, we prove a quantitative result for the number of sign changes for the sequence of q-exponents at primes in short intervals. Second, we investigate the growth of the q-exponents.

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Acknowledgements

I would like to thank The Institute of Mathematical Sciences, India, for providing excellent research facilities. I wish to express my gratitude to Prof. W. Kohnen for his invaluable comments on an earlier version of this paper. I am grateful to the referee for thorough perusal of this paper and his valuable suggestions.

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Authors and Affiliations

  1. The Institute of Mathematical Sciences, IV Cross Road, CIT Campus, Taramani, Chennai, 600113, India

    G. K. Viswanadham

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  1. G. K. Viswanadham
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Correspondence to G. K. Viswanadham.

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Funding was provided by Department of Atomic Energy, Government of India (IN).

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Viswanadham, G.K. On the q-Exponents of Generalized Modular Functions. Ramanujan J 44, 1–11 (2017). https://doi.org/10.1007/s11139-016-9880-3

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  • DOI: https://doi.org/10.1007/s11139-016-9880-3

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