Jiseong Kim

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20202022

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math.NT2020

On the asymptotics of the shifted sums of Hecke eigenvalue squares

Jiseong Kim

The purpose of this paper is to obtain asymptotics of shifted sums of Hecke eigenvalue squares on average. We show that for $X^{\frac{2}{3} + ε} < H < X^{1 - ε},$ there are constants $B…

math.NT2020

On Hecke eigenvalues of cusp forms in almost all short intervals

Jiseong Kim

Let $ψ$ be a function such that $ψ (x) \to \infty$ as $x \to \infty.$ Let $λ_{f} (n)$ be the $n$ -th Hecke eigenvalue of a fixed holomorphic cusp form $f$ for $SL(2,\m…