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math.NT2026
Explicit bounds for the prime number theorem
Andrew Fiori, Mikko Jaskari
We study the problem of finding tight explicit bounds on sums over zeros of -functions near the -line with a variety of zero-free regions and zero-density estimates. As an ap…
math.NT2026
Zero density theorems for short intervals
Andrew Fiori
We provide explicit bounds on the number of zeros for in short intervals near the edge of the critical strip. Ultimately we show that even in short intervals a positive proport…
math.NT2026
Bounds for Mertens Sums
Samuel Broadbent, Andrew Fiori, Habiba Kadiri +2
In this article we provide new bounds for the Mertens sums and products including and which provide superior exponential a…