has cardinality r ≥ 1. Let G be the F-rational points of a simple Chevalley group defined over F. In his thesis, Matsumoto [5] gave a beautiful construction for the metaplectic cover G of G, a… Expand

Let pn denote the n th smallest prime number, and let L denote the set of limit points of the sequence {(pn+1−pn)/logpn}n=1∞ of normalized differences between consecutive primes. We show that, for… Expand

A study of certain Hamiltonian systems has lead Y. Long to conjecture the existence of infinitely many primes of the form $p=2[\alpha n]+1$, where $1 0$ depends only on $\alpha$. We also prove a… Expand

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in International Mathematics Research Notices. The definitive publisher-authenticated version William D. Banks,… Expand

AbstractWe obtain asymptotic formulae for the number of primes p ≤ x for which the reduction modulo p of the elliptic curve $$
E_{a,b} :Y^2 = X^3 + aX + b
$$ satisfies certain “natural” properties,… Expand

Some of the results are rigorous and are based on recent advances in analytic number theory; some are conditional under certain widely believed conjectures; and others are purely heuristic in nature.Expand