1.2k citations
- California Institute of TechnologyUS11 papers
- Purdue University West LafayetteUS7 papers
- Scuola Normale SuperioreIT6 papers
- Princeton UniversityUS5 papers
- University of ArizonaUS5 papers
- University of CologneDE5 papers
- Cornell UniversityUS4 papers
- Jet Propulsion LaboratoryUS4 papers
- Lomonosov Moscow State UniversityRU4 papers
- Ames Research CenterUS3 papers
- Imperial College LondonGB3 papers
- National Radio Astronomy ObservatoryUS3 papers
6 papers · 1 filter
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…
Sums and products in finite fields: an integral geometric viewpoint
Derrick Hart, Alex Iosevich
We prove that if is such that then where $$A^2=\{a \cdot a': a,a'…
Sato--Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height
William D. Banks, Igor E. Shparlinski
We obtain asymptotic formulae for the number of primes for which the reduction modulo of the elliptic curve $$ \E_{a,b} : Y^2 = X^3 + aX + b $$ satisfies certain ``nat…
Uniform Distribution of Fractional Parts Related to Pseudoprimes
William D. Banks, Moubariz Z. Garaev, Florian Luca +1
We estimate exponential sums with the Fermat-like quotients $$ 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…
Almost all palindromes are composite
William D. Banks, Derrick N. Hart, Mayumi Sakata
We study the distribution of palindromic numbers (with respect to a fixed base ) over certain congruence classes, and we derive a nontrivial upper bound for the number of p…