3 citations · 6 across the 4 of their papers we have counts for
4 papers
On primitive Dirichlet characters and the Riemann hypothesis
William D. Banks, Ahmet M. Guloglu, C. Wesley Nevans
For any natural number , let be the set of primitive Dirichlet characters modulo . We show that if the Riemann hypothesis is true, then the inequality $|X'_{2n_k}|\le…
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 , where is a fixed irrational number. A…
Uniform Distribution of Fractional Parts Related to Pseudoprimes
William D. Banks, Moubariz Z. Garaev, Florian Luca +1
We estimate exponential sums with the Fermat-like quotients $$ f_g(n) = \frac{g^{n-1} - 1}{n} \mand h_g(n)=\frac{g^{n-1}-1}{P(n)}, $$ where and are positive integers, i…
Noncototients and Nonaliquots
William D. Banks, Florian Luca
Let and denote the Euler function and the sum of divisors function, respectively. In this paper, we give a lower bound for the number of positive integers $m\…