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Omega Results for Fourier Coefficients of Half-Integral Weight and Siegel Modular Forms

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Modular Forms and Related Topics in Number Theory (ICNT 2018)

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Abstract

We prove an \(\Omega \)-result for the Fourier coefficients of a half-integral weight cusp form of arbitrary level, nebentypus and weights. In particular, this implies that the analogue of the Ramanujan-Petersson conjecture for such forms is essentially the best possible. As applications, we show similar \(\Omega \)-results for Fourier coefficients of Siegel cusp forms of any degree and on Hecke congruence subgroups.

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Acknowledgements

The author thanks the referee for useful comments. He also thanks IISc. Bangalore, DST (India) and UGC centre for advanced studies for financial support. During the preparation of this work the author was supported by a MATRICS grant MTR/2017/000496 from DST-SERB, India, and during the final revision of the paper by a Humboldt fellowship from Alexander von Humboldt Foundation.

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Authors and Affiliations

  1. Indian Institute of Science, Bengaluru, 560012, India

    Soumya Das

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  1. Soumya Das
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Correspondence to Soumya Das .

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Editors and Affiliations

  1. Statistics and Applied Mathematics, CUTN, Thiruvarur, India

    B. Ramakrishnan

  2. Faculty of Mathematics, Computer Science, and Natural Sciences, RWTH Aachen University, Aachen, Germany

    Bernhard Heim

  3. School of Mathematical Sciences, NISER, Bhubaneswar, Odisha, India

    Brundaban Sahu

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Das, S. (2020). Omega Results for Fourier Coefficients of Half-Integral Weight and Siegel Modular Forms. In: Ramakrishnan, B., Heim, B., Sahu, B. (eds) Modular Forms and Related Topics in Number Theory. ICNT 2018. Springer Proceedings in Mathematics & Statistics, vol 340. Springer, Singapore. https://doi.org/10.1007/978-981-15-8719-1_5

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