8 papers · 1 filter
Functional Equations Characterize Dirichlet Characters
Ghaith Hiary, Ali Saraeb
We prove a converse theorem for functional equations of Dirichlet -functions. Under mild assumptions, we prove that these functional equations for -series of the form $\sum_{…
Unconditional estimates on the argument of Dirichlet -functions with applications to low-lying zeros
Ghaith Hiary, Tianyu Zhao
We make explicit a result of Selberg on the argument of Dirichlet -functions averaged over non-principal characters modulo a prime . As a corollary, we show for all sufficien…
A method for verifying the generalized Riemann hypothesis
Ghaith Hiary, Summer Ireland, Megan Kyi
Riemann numerically approximated at least three zeta zeros. According to Edwards, Riemann even took steps to verify that the lowest zero he computed was indeed the first zeta zero.…
Counting sign changes of partial sums of random multiplicative functions
Nick Geis, Ghaith Hiary
Let be a Rademacher random multiplicative function. Let be the partial sum of . Let denote the number of sign changes of u…
Explicit bounds for the Riemann zeta-function on the 1-line
Ghaith A. Hiary, Nicol Leong, Andrew Yang
Explicit estimates for the Riemann zeta-function on the -line are derived using various methods, in particular van der Corput lemmas of high order and a theorem of Borel and Car…
A Generalization of Lehman's Method
Jonathon Hales, Ghaith Hiary
A new deterministic algorithm for finding square divisors, and finding -power divisors in general, is presented. This algorithm is based on Lehman's method for integer factoriza…