Functiones et Approximatio Commentarii Mathematici

Some problems of analytic number theory on arithmetic semigroups

Glyn Harman and Kaisa Matomäki

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Let $\mathcal{E}$ be a set of primes with density $\tau > 0$ in the set of primes. Write $\mathcal{A}$ for the set of positive integers composed solely of primes from $\mathcal{E}$. We discuss the distribution of the integers from $\mathcal{A}$ in short intervals, and whether for fixed $k \in \mathbb{Z}$ there are solutions to $m+k = p$ with $m \in \mathcal{A}$, where $p$ denotes a prime, or $m+k=n$ where $n$ has a large prime factor ($>n^{\xi}$ for $\xi > \tfrac{1}{2}$

Article information

Funct. Approx. Comment. Math., Volume 38, Number 1 (2008), 21-39.

First available in Project Euclid: 18 December 2008

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Zentralblatt MATH identifier

Primary: 11N25: Distribution of integers with specified multiplicative constraints
Secondary: 11N36: Applications of sieve methods

greatest prime factors distribution in short intervals


Harman, Glyn; Matomäki, Kaisa. Some problems of analytic number theory on arithmetic semigroups. Funct. Approx. Comment. Math. 38 (2008), no. 1, 21--39. doi:10.7169/facm/1229624649.

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