19 citations · 99 across the 36 of their papers we have counts for
5 papers · 1 filter
Sato--Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height
William D. Banks, Igor E. Shparlinski
We obtain asymptotic formulae for the number of primes for which the reduction modulo of the elliptic curve $$ \E_{a,b} : Y^2 = X^3 + aX + b $$ satisfies certain ``nat…
Character sums with Beatty sequences on Burgess-type intervals
William D. Banks, Igor E. Shparlinski
We estimate multiplicative character sums taken on the values of a non-homogeneous Beatty sequence , where , and is irrational. Our bounds…
Density of non-residues in Burgess-type intervals and applications
W. D. Banks, M. Z. Garaev, D. R. Heath-Brown +1
We show that for any fixed $\eps>0$, there are numbers and with the following property: for every prime and every integer such that $p^{1/(4\sqrt{e}…
Integers without divisors from a fixed arithmetic progression
William D. Banks, John B. Friedlander, Florian Luca
Let a be an integer and q a prime number. In this paper, we find an asymptotic formula for the number of positive integers n < x with the property that no divisor d > 1 of n lies i…
Integers with a large smooth divisor
William D. Banks, Igor E. Shparlinski
We study the function that counts the number of positive integers which have a divisor with the property that for every prime dividing . W…