59 citations · 137 across the 25 of their papers we have counts for
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Small gaps between almost primes, the parity problem, and some conjectures of Erdős on consecutive integers II
Daniel A. Goldston, Sidney W. Graham, Apoorva Panidapu +3
This paper is intended as a sequel to a paper arXiv:0803.2636 written by four of the coauthors here. In the paper, they proved a stronger form of the Erdős-Mirksy conjecture which…
A new explicit formula in the additive theory of primes with applications II. The exceptional set in Goldbach's problem
Janos Pintz
Improving earlier estimates of several authors we show that the number E(X) of Goldbach exceptional even integers (that is, even integers which cannot be written as the sum of two…
A new explicit formula in the additive theory of primes with applications I. The explicit formula for the Goldbach and Generalized Twin Prime Problems
Janos Pintz
A new explicit formula is proved for the contribution of the major arcs in the Goldbach and Generalized Twin Prime Problem, in which the level of the major arcs can be chosen very…
Some new density theorems for Dirichlet L-functions
Janos Pintz
We prove some new log-free density theorems for zeros of Dirichlet L-functions (which accordingly are more sharp than earlier ones near to the boundary line of the critical strip).…
A note on the distribution of normalized prime gaps
János Pintz
Let us denote the nth difference between consecutive primes by d_n. The Prime Number Theorem clearly implies that d_n is logn on average. Paul Erdős conjectured about 60 years ago…
Patterns of primes in arithmetic progressions
Janos Pintz
We show that there exists a bounded pattern of m consecutive primes for any m>0, that means a tuple H_m of m distinct non-negative integers h_i (i=1,2,...m) such that its translati…