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math.NT2025
A round of Pintz to celebrate oscillations in sums
Daniel R. Johnston, Tim Trudgian
We explore a method, going back to Landau and developed by Pintz, for connecting sums of arithmetic functions with zero-free regions for -functions. In particular, we make expli…
math.NT2025
An effective Bombieri-Vinogradov error term for sifting problems
Daniel R. Johnston
In number theory, many major results related to the additive properties of primes are proven using the methods of sieve theory. However, in nearly every case, the existing proofs o…