It is an open question as to whether the prime numbers contain
the sum A+B of two infinite sets of natural numbers A, B (although
results of this type are known assuming the Hardy-Littlewood prime
tuples conjecture). Using the Maynard sieve and the...
The "intersectivity lemma" states that if a ∈
(0,1) and A_n, n ∈ N, are measurable sets in a
probability space (X,m) satisfying m(A_n) ≥ a for
all n, then there exist a subsequence n_k, k ∈ N, which
has positive upper density and such that the...
A density theorem for L-functions is quantitative measure of the
possible failure of the Riemann Hypothesis. In his 1990 ICM talk,
Sarnak introduced the notion of density theorems for families of
automorphic forms, measuring the possible failure of...