W. Banks

activity

20042026

most citedDensity of non-residues in Burgess-type intervals and applications

19 citations · 99 across the 36 of their papers we have counts for

collaborators

Showing 2007Show all

3 papers · 1 filter

math.NT2007★ 4 cited

The Nicolas and Robin inequalities with sums of two squares

William D. Banks, Derrick N. Hart, Pieter Moree +1

In 1984, G. Robin proved that the Riemann hypothesis is true if and only if the Robin inequality $σ (n) < e^{γ} n lo g lo g n$ holds for every integer $n > 5040$ , where $σ (n)$ is the sum of…

math.NT2007★ 3 cited

Prime numbers with Beatty sequences

William D. Banks, Igor E. Shparlinski

A study of certain Hamiltonian systems has lead Y. Long to conjecture the existence of infinitely many primes of the form $p = 2 [α n] + 1$ , where $1 < α < 2$ is a fixed irrational number. A…

math.NT2007★ 8 cited

Representations of integers as sums of primes from a Beatty sequence

William D. Banks, Ahmet M. Guloglu, C. Wesley Nevans

We study the problem of representing integers as sums of prime numbers from a fixed Beatty sequence $B_{α, β}$ , where $α > 1$ is irrational and of finite type.