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math.NT2021
Large sieve estimate for multivariate polynomial moduli and applications
Karin Halupczok, Marc Munsch
We prove large sieve inequalities with multivariate polynomial moduli and deduce a general Bombieri--Vinogradov type theorem for a class of polynomial moduli having a sufficient nu…
math.NT2021
Difference sets and the metric theory of small gaps
Christoph Aistleitner, Daniel El-Baz, Marc Munsch
Let be a sequence of distinct positive integers. In a recent paper Rudnick established asymptotic upper bounds for the minimal gaps of $\{a_n α\bmod 1, 1 \leq n…
math.NT2021
Additive energy and a large sieve inequality for sparse sequences
Roger C. Baker, Marc Munsch, Igor E. Shparlinski
We consider the large sieve inequality for sparse sequences of moduli and give a general result depending on the additive energy (both symmetric and asymmetric) of the sequence of…