Ping Xi

Quadratic polynomials at prime arguments

For a fixed quadratic irreducible polynomial f with no fixed prime factors at prime arguments, we prove that there exist infinitely many primes p such that f(p) has at most 4 prime factors, improving a classical result of Richert who requires 5 in place of 4. Denoting by

On triple correlations of Fourier coefficients of cusp forms

P^+(n)

Arithmetic exponent pairs for algebraic trace functions and applications

P+(n) the greatest prime factor of n, it is also proved that

Sign changes of Kloosterman sums with almost prime moduli

P^+(f(p))>p^{0.847}

A quadratic analogue of Titchmarsh divisor problem

P+(f(p))>p0.847 infinitely often.

Large Sieve Inequalities for Algebraic Trace Functions

In this note, we deduce an asymptotic formula for even power moments of Kloosterman sums based on the important work of N. M. Katz on Kloosterman sheaves. In a similar manner, we can also obtain an upper bound for odd power moments. Moreover, we shall give an asymptotic formula for odd power moments of absolute Kloosterman sums. Consequently, we find that there are infinitely many