4 papers
The Legendre Approximation and Arithmetic Bias
Ghaith Hiary, Megan Paasche
An interesting episode in the history of the prime number theorem concerns a formula proposed by Legendre for counting the primes below a given bound. We point out that arithmetic…
New Formulas for the Riemann Zeta Function
Aditya Akula, Ghaith Hiary
A new method for continuing the usual Dirichlet series that defines the Riemann zeta function is presented. Numerical experiments demonstrating the computational efficacy of…
An improved explicit estimate for
Ghaith A. Hiary, Dhir Patel, Andrew Yang
An explicit subconvex bound for the Riemann zeta function on the critical line is proved. Previous subconvex bounds relied on an incorrect version of the Kusmin-L…
A fast amortized algorithm for computing quadratic Dirichlet -functions
Ghaith A. Hiary
An algorithm to compute Dirichlet -functions for many quadratic characters is derived. The algorithm is optimal (up to logarithmic factors) provided that the conductors of the c…