Some problems of analytic number theory on arithmetic semigroups

Harman, Glyn; Matomäki, Kaisa

Funct. Approx. Comment. Math., Tome 38 (2008) no. 1, p. 21-39 / Harvested from Project Euclid

Résumé

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 $\xi > \tfrac{1}{2}$

Publié le : 2008-01-15
Classification: greatest prime factors, distribution in short intervals, 11N25, 11N36

@article{1229624649,
     author = {Harman, Glyn and Matom\"aki, Kaisa},
     title = {Some problems of analytic number theory on arithmetic semigroups},
     journal = {Funct. Approx. Comment. Math.},
     volume = {38},
     number = {1},
     year = {2008},
     pages = { 21-39},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1229624649}
}

Harman, Glyn; Matomäki, Kaisa. Some problems of analytic number theory on arithmetic semigroups. Funct. Approx. Comment. Math., Tome 38 (2008) no. 1, pp.  21-39. http://gdmltest.u-ga.fr/item/1229624649/