A common combinatorial principle underlies Riemann's formula, the Chebyshev phenomenon, and other subtle effects in comparative prime number theory. I.
A conjecture of Erdös in number theory
A further note on the P.N.T. error term
A generalisation of Artin's conjecture for primitive roots
A higher rank Selberg sieve and applications
We develop an axiomatic formulation of the higher rank version of the classical Selberg sieve. This allows us to derive a simplified proof of the Zhang and Maynard-Tao result on bounded gaps between primes. We also apply the sieve to other subsequences of the primes and obtain bounded gaps in various settings.
A mean value theorem of Bombieri's type
A new equidistribution property of norms of ideals in given classes
A new method in the elementary theory of primes
A note on a theorem of Hardy and Littlewood
A note on large gaps between consecutive prime numbers
A note on large gaps between prime numbers
A note on numbers with good factorization properties
A note on primes between consecutive powers
A note on Selberg sieve
A note on small gaps between primes in arithmetic progressions
We implement the Maynard-Tao method of detecting primes in tuples to investigate small gaps between primes in arithmetic progressions, with bounds that are uniform over a range of moduli.
A Note on the Differences Between Consecutive Primes.
A prime number theorem in the theory of the Riemann zeta function.
A probabilistic setting for prime number theory
A Proof of the Prime Number Summation Formula Without Assuming the Riemann Hypothesis.
A Proof of the Prime Number Summation Formula Without Assuming the Riemann Hypothesis. (Short Communication).