4 citations · 4 across the 6 of their papers we have counts for
6 papers
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 mult…
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…
New explicit bounds for Mertens function and the reciprocal of the Riemann zeta-function
Ethan S. Lee, Ethan Simpson Lee, Nicol Leong
IWe prove new unconditional and explicit upper bounds for the reciprocal of the Riemann zeta function in the critical strip, of the orders , $(\log t)^{11/12}(\lo…
Primitive element pairs with a prescribed trace in the cubic extension of a finite field
Andrew R. Booker, Stephen D. Cohen, Nicol Leong +1
We prove that for any prime power , the cubic extension of the finite field contains a primitive element such that $ξ+ξ^{-1}…
Primitive elements with prescribed traces
Andrew R. Booker, Stephen D. Cohen, Nicol Leong +1
Given a prime power and a positive integer , let denote the finite field with elements. Also let be arbitrary members of the ground field $\…
Sums of reciprocals and the three distance theorem
Victor Beresnevich, Nicol Leong
In this paper we investigate the sums of reciprocals to an arithmetic progression taken modulo one, that is sums of , where and are real parameters and $\{\,…