Large Hecke eigenvalues and an Omega result for non-Saito–Kurokawa lifts

Abstract

We prove a result on the distribution of Hecke eigenvalues, \(\mu _F(p^r)\) (for \(r=1,2\) or 3) of a non-Saito–Kurokawa lift F of degree 2. As a consequence, we obtain an Omega result for the Hecke eigenvalues for such an F, which is the best possible in terms of orders of magnitude.

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Correspondence to Pramath Anamby.

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S.D. was supported by a Humboldt Fellowship from the Alexander von Humboldt Foundation at Universität Mannheim during the preparation of the paper, and thanks both for the generous support and for providing excellent working conditions. He also thanks IISc, Bangalore, DST (India) and UGC centre for advanced studies for financial support. During the preparation of this work S.D. was supported by a MATRICS Grant MTR/2017/000496 from DST-SERB, India. P.A. and R.P. were supported by IISc Research Associateship during the preparation of this article and thank IISc, Bangalore for the support.

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Anamby, P., Das, S. & Pal, R. Large Hecke eigenvalues and an Omega result for non-Saito–Kurokawa lifts. Ramanujan J (2020). https://doi.org/10.1007/s11139-020-00328-0

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Keywords

  • Hecke eigenvalues
  • Non-Saito–Kurokawa lifts
  • Omega results

Mathematics Subject Classification

  • Primary 11F46