Abstract
We study the angle changes of Fourier coefficients of cusp forms and q-exponents of generalized modular functions at primes. More precisely, we prove that both these subsequences, under certain conditions, fall infinitely often outside any given wedge \(\mathcal {W}(\theta _1, \theta _2):=\{re^{i\theta }: r>0, \theta \in [\theta _1,\theta _2]\}\) with \(0\le \theta _2-\theta _1< \pi \).
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Acknowledgements
We are grateful to Prof. M. Ram Murty for his helpful comments on an earlier version of the paper. We sincerely thank the referee for his/her careful reading of the manuscript and for providing many useful comments which improves the presentation of the paper.
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Funding was provided by the Department of Atomic Energy, Government of India.
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Kumar, B., Viswanadham, G.K. Angular changes of Fourier coefficients at primes. Ramanujan J 49, 641–651 (2019). https://doi.org/10.1007/s11139-018-0059-y
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DOI: https://doi.org/10.1007/s11139-018-0059-y