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math.NT2026
A criterion for weighted uniform distribution along functions from a Hardy field
Michael Reilly
A classical theorem of Boshernitzan states that if is a function which belongs to a Hardy field and which satisfies for some , then t…
math.NT2026
Weighted averages of arithmetic functions and applications to equidistribution and ergodic theory
Vitaly Bergelson, Michael Reilly, Florian K. Richter
For a wide range of functions , we establish a general result for estimating weighted averages of the form\[\mathbb{E}^{W}_{n \le N} f(\vartheta(n))…