arXiv subjects

Nagarjuna Chary Addanki

Publications and source records attributed to Nagarjuna Chary Addanki.

3 recordsLinked to original sources

arXiv2026

Hecke Eigenvalues of Ikeda Lifts

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 $p$.

math.NT↗

arXiv2024

On Signs of eigenvalues of Modular forms satisfying Ramanujan Conjecture

Let $F \in S_{k_1}(Γ^{(2)}(N_1))$ and $G \in S_{k_2}(Γ^{(2)}(N_2))$ be two Siegel cusp forms over the congruence subgroups $Γ^{(2)}(N_1)$ and $Γ^{(2)}(N_2)$ respectively. Assume that they are Hecke eigenforms in different eigenspaces and satisfy the Generalized Ramanujan Conjecture. Let $λ_F(p)$ denote the eigenvalue of $F$ with respect to the Hecke operator $T(p)$. In this article, we compute a lower bound for the density of the set of primes, $\{ p : λ_F(p) λ_G(p) < 0 \}.$

math.NT↗

arXiv2024

On Signs of Hecke eigenvalues of Ikeda lifts

Let $F$ be an Ikeda lift, $λ_F(m)$ be the eigenvalue corresponding to the Hecke operator $T(m)$. We show that $λ_F(p)$ 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 $λ_F(p^r)$ is positive for all $p>c_r$.

math.NT↗