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 2016Show all

3 papers · 1 filter

math.NT2016

Consecutive primes and Beatty sequences

William D. Banks, Victor Z. Guo

Fix irrational numbers $α, α^> 1$ of finite type and real numbers $β, β^\geq 0$ , and let $B$ and $B^$ be the Beatty sequences $$ B:=(\lfloorαm+β\rfloor)_{m\ge 1}\quad\text{an…

math.NT2016★ 4 cited

Bounds on short character sums and L-functions for characters with a smooth modulus

William Banks, Igor Shparlinski

We combine a classical idea of Postnikov (1956) with the method of Korobov (1974) for estimating double Weyl sums, deriving new bounds on short character sums when the modulus $q$ …

math.NT2016

On the number of distinct quadratic fields generated by the Shanks sequence

William D. Banks, Igor E. Shparlinski

Let $g > 1$ be an integer and $f (X) \in Z [X]$ a polynomial of positive degree with no multiple roots, and put $u (n) = f (g^{n})$ . In this note, we study the sequence of quadratic…