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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Primes in arithmetic progression and uniform distribution

Author: M. A. Wodzak
Journal: Proc. Amer. Math. Soc. 122 (1994), 313-315
MSC: Primary 11K06; Secondary 11L20, 11N13
MathSciNet review: 1233985
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Abstract: Let f be an entire, non-polynomial function with real coefficients. Let $ \tilde p$ run through the primes such that $ \tilde p \equiv h \bmod k,(h,k) = 1$, and let $ M > 1$. If there exists $ \alpha \in (1,4/3)$ such that $ \vert f(z)\vert \leq \exp ({(\log \vert z\vert)^\alpha })$ for all $ \vert z\vert > M$, then the sequence $ \{ f(\tilde p)\} $ is uniformly distributed modulo 1.

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PII: S 0002-9939(1994)1233985-1
Article copyright: © Copyright 1994 American Mathematical Society

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