Showing papers by "Henryk Iwaniec published in 1984"
Journal Article•
TL;DR: In this paper, the Seiberg zeta function is defined for the case of the modular group F = PSL(2, Z) and its most fascinating property is that the analogue of the Riemann hypothesis is true.
Abstract: In the middle of the fifties A. Seiberg [18] introduced to number theory the celebrated trace formula and in connection with this he introduced a zeta-fimction which mimics the classical zeta-function of Riemann in various aspects. Its most fascinating property is that the analogue of the Riemann hypothesis is true. In this paper we consider the case of the modular group F = PSL(2, Z). The Seiberg zeta-function is defined by
83 citations
TL;DR: In this article, it was shown that for the difference between consecutive primes, the inequality p ≥ 1−p+1−p======n−1−n======n ≥ 2π(n−y)>y/(100 logx) is π(x)−π(x−y), where π is the number of primes not exceeding x.
Abstract: Let π(x) stand for the number of primes not exceedingx. In the present work it is shown that if 23/42≤Θ≤1,y≤x
θ andx>x(Θ) then π(x)−π(x−y)>y/(100 logx). This implies for the difference between consecutive primes the inequalityp
n+1−p
n
≪p
23/42
.
49 citations
26 citations