The number-theoretic work of Paul Turán
The pair correlation of zeros of Dirichlet L-functions and primes in arithmetic progressions.
The Piltz divisor problem in number fields: An improved lower bound by Soundararajan's method
The polynomial captures its primes.
The prime number theorem for Beurling's generalized numbers. New cases
The propinquity of divisors
The quickest proof of the prime number theorem
The range of the sum-of-proper-divisors function
Answering a question of Erdős, we show that a positive proportion of even numbers are in the form s(n), where s(n) = σ(n) - n, the sum of proper divisors of n.
The representation of primes by cubic polynomials
The representation of primes by quadratic and cubic polynomials
The “Riemann hypothesis” for the Hawkins random Sieve
The Romanoff theorem revisited
The Rosser-Iwaniec sieve in number fields, with an application
The Selberg-Delange method in short intervals with an application
We establish a general mean value result for arithmetic functions over short intervals with the Selberg-Delange method. As an application, we generalize the Deshouillers-Dress-Tenenbaum arcsine law on divisors to the short interval case.
The sequences of prime divisors of integers
The Siegel-Walfisz theorem for Rankin-Selberg L-functions associated with two cusp forms
The sieve of Eratosthenes-Legendre
The spectral mean value for linear forms in twisted coefficients of cusp forms
The Square Sieve and Consecutive Square-Free Numbers.
The sum of digits of