29 citations · 39 across the 8 of their papers we have counts for
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math.NT2014★ 8 cited
A Brun-Titchmarsh inequality for weighted sums over prime numbers
Jan Büthe
We prove explicit upper bounds for weighted sums over prime numbers in arithmetic progressions with slowly varying weight functions. The results generalize the well-known Brun-Titc…
math.NT2014★ 29 cited
Estimating and related functions under partial RH assumptions
Jan Büthe
The aim of this paper is to give a direct interpretation of the validity of the Riemann hypothesis up to a certain height in terms of the prime-counting function . This i…