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On algebraic twists with composite moduli

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Abstract

We study bounds for algebraic twists sums of automorphic coefficients by trace functions of composite moduli.

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Notes

  1. This may require the Ramanujan–Petersson conjecture.

  2. Possibly combined with the previous one.

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Acknowledgements

Part of this work was inspired by [3]. The first named author would like to thank K. Aggarwal, R. Holowinsky, and Q. Sun for generously sharing their ideas while working on that project. We thank P. Sharma for a helpful comment on an earlier version of this manuscript and the referees for their helpful suggestions. As mentioned in the beginning of this paper, this work is dedicated to the memory of Chandra Sekhar Raju who passed away one year ago, in India, surrounded by his family. Before his premature passing, Chandra was a postdoc in the TAN group at EPFL and before that, a PhD student at Stanford under the supervision of K. Soundararajan. Chandra was not only a gentle soul but also a wonderful colleague, full of ideas, with whom we had countless discussions; several of his ideas are to be found in this paper. It is therefore with both sadness and gratitude that we dedicate this paper to the memory of him.

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Authors and Affiliations

  1. Data Science Institute, Shandong University, Jinan, 250100, China

    Yongxiao Lin

  2. EPFL/MATH/TAN, Station 8, 1015, Lausanne, Switzerland

    Philippe Michel

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  1. Yongxiao Lin
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Both authors contributed to the manuscript equally.

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Correspondence to Yongxiao Lin.

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In memory of Chandra Sekhar Raju

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Yongxiao Lin was partially supported by the National Key R &D Program of China (No. 2021YFA1000700). Philippe Michel was partially supported by the SNF (Grant 200021_197045)

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Lin, Y., Michel, P. On algebraic twists with composite moduli. Ramanujan J 63, 803–837 (2024). https://doi.org/10.1007/s11139-023-00789-z

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