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math.NT2023
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…
math.NT2023
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…