2 citations · 4 across the 5 of their papers we have counts for
5 papers
Explicit Subconvexity Estimates for Dirichlet -functions
Forrest J. Francis
Given a Dirichlet character modulo and its associated -function, , we provide an explicit version of Burgess' estimate for . We use partial summation…
Explicit Improvements to the Burgess Bound Via Pólya-Vinogradov
Matteo Bordignon, Forrest Francis
We make explicit a theorem of Fromm and Goldmakher [arXiv:1706.03002], which states that one can improve Burgess' bound for short character sums simply by improving the leading con…
Additive Representations of Natural Numbers
Forrest J. Francis, Ethan S. Lee
Every natural number greater than two may be written as the sum of a prime and a square-free number. We establish several generalisations of this, by placing divisibility condition…
An Investigation Into Several Explicit Versions of Burgess' Bound
Forrest J. Francis
Let be a Dirichlet character modulo , a prime. In applications, one often needs estimates for short sums involving . One such estimate is the family of bounds known as \e…
Euler's Function on Products of Primes in Progressions
Amir Akbary, Forrest J. Francis
We study generalizations of some results of Jean-Louis Nicolas regarding the relation between small values of Euler's function and the Riemann Hypothesis. Among other things…