3 papers
math.NT2024
New bounds and progress towards a conjecture on the summatory function of
Daniel R. Johnston, Nicol Leong, Sebastian Tudzi
In this article, we study the summatory function \begin{equation*} W(x)=\sum_{n\leq x}(-2)^{Ω(n)}, \end{equation*} where counts the number of prime factors of , with mu…
math.NT2024
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…
math.NT2024
New explicit bounds for Mertens function and the reciprocal of the Riemann zeta-function
Ethan S. Lee, Nicol Leong
In this paper, we establish new explicit bounds for the Mertens function . In particular, we compare against a short-sum over the non-trivial zeros of the Riemann zeta…