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arXiv · 2401.08855

On Signs of Hecke eigenvalues of Ikeda lifts

Nagarjuna Chary Addanki
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Abstract

Let $F$ be an Ikeda lift, $\lambda_F(m)$ be the eigenvalue corresponding to the Hecke operator $T(m)$. We show that $\lambda_F(p)$ is positive for all large enough primes $p$. This is proved for Ikeda lifts of all genus. The second result is specific for genus 4 Ikeda lifts. If $F$ is genus 4 Ikeda lift, we show that, given $r$ there exists a constant $c_r$ such that $\lambda_F(p^r)$ is positive for all $p>c_r$.

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Nagarjuna Chary Addanki. 2024-01-16. On Signs of Hecke eigenvalues of Ikeda lifts. https://arxiv.org/abs/2401.08855

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