On a conjecture of Yiming Long
On a ternary quadratic form over primes
On an equation with prime numbers
On Hecke eigenvalues at primes of the form [g(n)]
We study the average of the Fourier coefficients of a holomorphic cusp form for the full modular group at primes of the form [g(n)].
On instances of Fox’s integral equation connection to the Riemann zeta function
We consider some applications of the singular integral equation of the second kind of Fox. Some new solutions to Fox’s integral equation are discussed in relation to number theory.
On Linnik's theorem on Goldbach numbers in short intervals and related problems
Linnik proved, assuming the Riemann Hypothesis, that for any , the interval contains a number which is the sum of two primes, provided that is sufficiently large. This has subsequently been improved to the same assertion being valid for the smaller gap , the added new ingredient being Selberg’s estimate for the mean-square of primes in short intervals. Here we give another proof of this sharper result which avoids the use of Selberg’s estimate and is therefore more in the spirit of Linnik’s...
On the existence of a non-zero lower bound for the number of Goldbach partitions of an even integer.
On the Vinogradov bound in the three primes Goldbach conjecture