For every even integerN , denote byD(N) andD1,2(N) the number of representations of N as a sum of two primes and as a sum of a prime and an integer having at most two prime factors, respectively. In… Expand

Fouvry and Iwaniec's method ([6], [11]) for exponential sums with monomials uses, in a crucial way, a spacing lemma for t(m, q) := (m + q)α − (m − q)α. By introducing a technique on integer points… Expand

In this paper, we establish a general mean value result of arithmetic functions over short intervals with the Selberg-Delange method. As an application, we generalize the… Expand

In this paper, we establish a large sieve inequality of Elliott-MontgomeryVaughan type for Fourier coefficients of newforms. As applications, we give a significant improvement on the principal result… Expand

We prove that for almost all real primitive characters χd of modulus |d|, the least positive integer nχd at which χd takes a value not equal to 0 and 1 satisfies nχd ¿ log |d|, and give a quite… Expand

This short note improves some of the results of studied asymptotic behaviour of the quantity S f ( x) under three different types of assumptions on f.Expand