Primes in arithmetic progression and uniform distribution

Wodzak, M. A.

doi:10.1090/S0002-9939-1994-1233985-1

Primes in arithmetic progression and uniform distribution
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by M. A. Wodzak PDF

Proc. Amer. Math. Soc. 122 (1994), 313-315 Request permission

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 $|f(z)| \leq \exp ({(\log |z|)^\alpha })$ for all $|z| > M$, then the sequence $\{ f(\tilde p)\}$ is uniformly distributed modulo 1.

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