5 citations · 5 across the 9 of their papers we have counts for
9 papers · 1 filter
Minimal zero-free regions for results on primes between consecutive perfect th powers
Ethan Simpson Lee
We compute minimal zero-free regions for the Riemann zeta-function of the Littlewood form which ensure there is always a prime between consecutive perfect th powers. Our computa…
On the sum of a prime and a square-free number co-prime to any integer with at most two prime factors
Ethan S. Lee, Rowan O'Clarey
Every natural number greater than can be written as the sum of a prime and a square-free number, and recent work has imposed additional divisibility conditions on the square-fr…
On the error in the prime number theorem in short intervals
Ethan Simpson Lee
Assuming the Riemann Hypothesis, we derive explicit bounds for the error terms in short interval analogues of the prime number theorem using a new smoothing argument. Our results i…
Sharper bounds for the error in the prime number theorem assuming the Riemann Hypothesis
Ethan Simpson Lee, Paweł Nosal
In this paper, we establish new bounds for classical prime-counting functions. All of our bounds are explicit and assume the Riemann Hypothesis. First, we prove that a…
On the constants in Mertens' theorems for primes in arithmetic progressions
Daniel Keliher, Ethan Simpson Lee
A 1976 result from Norton may be used to give an asymptotic (but not explicit) description of the constant in Mertens' second theorem for primes in arithmetic progressions. Assumin…
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…
On the number of integral ideals in a number field
Ethan Simpson Lee
We update Sunley's explicit estimate for the ideal-counting function, which is the number of integral ideals of bounded norm in a number field.
Mertens' Third Theorem for Number Fields: A New Proof, Cramér's Inequality, Oscillations, and Bias
Shehzad Hathi, Ethan S. Lee
The first result of our article is another proof of Mertens' third theorem in the number field setting, which generalises a method of Hardy. The second result concerns the sign of…
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…