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<p>A well known result of Breulmann states that Hecke eigenvalues of Saito–Kurokawa lifts are positive. In this article, we show that the Hecke eigenvalues of an Ikeda lift at primes are positive. This improves a recent result of Addanki. Further, we derive lower and upper bounds of these Hecke eigenvalues for all primes <i>p</i>. One of the main ingredients involves expressing the Hecke eigenvalues of an Ikeda lift in terms of certain reciprocal polynomials.</p>

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On Hecke eigenvalues of Ikeda lifts

  • 期刊论文

  • 发表日期：

    2025年3月21日

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  • Sanoli Gun,
  • Sunil Naik

摘要

A well known result of Breulmann states that Hecke eigenvalues of Saito–Kurokawa lifts are positive. In this article, we show that the Hecke eigenvalues of an Ikeda lift at primes are positive. This improves a recent result of Addanki. Further, we derive lower and upper bounds of these Hecke eigenvalues for all primes p. One of the main ingredients involves expressing the Hecke eigenvalues of an Ikeda lift in terms of certain reciprocal polynomials.