Year: 2026
Type: preprint
Abstract: In this paper, we study the Hecke eigenvalues of Ikeda lifts. Using the spherical map for the Hecke algebra of the symplectic group, we obtain an explicit formula for the eigenvalues $λ_F(p^r)$. From this formula, we show that $λ_F(p^r)$ can be written as a polynomial in $p^{\pm 1/2}$ with a positive leading term. Furthermore, we prove that the coefficients of this polynomial are bounded and, as a consequence, the Hecke eigenvalues $λ_F(p^r)$ are positive for all sufficiently large primes $p$.
Source: arXiv (Cornell University)
Authors: Addanki, Nagarjuna Chary, Pitale, Ameya
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161586342