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math.NT2021
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…
math.NT2021
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…