6 papers · 1 filter
On the Rankin-Selberg problem in families
Jiseong Kim
In this paper, we investigate the Rankin-Selberg problem over short intervals in families of holomorphic modular forms and Hecke-Maass cusp forms. Our investigation assumes a Linde…
Approximations of Hecke-Maass -Functions by short Dirichlet polynomials
Jiseong Kim
We study averages of -functions associated with Hecke-Maass cusp forms for , multiplied by Dirichlet polynomials built from the Fourier coefficients of the cus…
Applications of zero-free regions on averages and shifted convolution sums of Hecke eigenvalues
Jiseong Kim
By assuming Vinogradov-Korobov type zero-free regions and the generalized Ramanujan-Petersson conjecture, we establish nontrivial upper bounds for almost all short sums of Fourier…
On sum of Hecke eigenvalue squares over primes in very short intervals
Jiseong Kim
Let be a fixed positive number, let be a sufficiently large number. In this paper, we study the second moment of the sum of Hecke eigenvalues over primes in short interva…
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 there are constants $B…
On Hecke eigenvalues of cusp forms in almost all short intervals
Jiseong Kim
Let be a function such that as Let be the -th Hecke eigenvalue of a fixed holomorphic cusp form for $SL(2,\m…