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Jan Büthe (2014)
Acta Arithmetica
We prove explicit upper bounds for weighted sums over prime numbers in arithmetic progressions with slowly varying weight functions. The results generalize the well-known Brun-Titchmarsh inequality.
P. Shiu (1980)
Journal für die reine und angewandte Mathematik
Gica, Alexandru (2007)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
Jürgen Hinz (1988)
Acta Arithmetica
Kaisa Matomäki (2009)
Acta Arithmetica
Deniz A. Kaptan (2016)
Acta Arithmetica
We implement the Maynard-Tao method of detecting primes in tuples to investigate small gaps between primes in arithmetic progressions, with bounds that are uniform over a range of moduli.
Yoichi Motohashi (1970)
Acta Arithmetica
Ming-Chit Liu, Tianze Wang (1998)
Acta Arithmetica
H. Stark (1971)
Acta Arithmetica
Akbik, Safwan (1991)
International Journal of Mathematics and Mathematical Sciences
Henryk Iwaniec (1978)
Inventiones mathematicae
R. Vaughan (1980)
Acta Arithmetica
Bordellés, Olivier (2005)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Terence Tao (2006)
Collectanea Mathematica
We describe some of the machinery behind recent progress in establishing infinitely many arithmetic progressions of length k in various sets of integers, in particular in arbitrary dense subsets of the integers, and in the primes.
E. Grosswald (1980)
Journal für die reine und angewandte Mathematik
Stuart Clary, Jacek Fabrykowski (2004)
Czechoslovak Mathematical Journal
In this paper we establish the distribution of prime numbers in a given arithmetic progression for which is squarefree.
Tom M. Apostol (1977)
Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
Stephan Baier, Sawian Jaidee, Shaun Stevens, Thomas Ward (2013)
Acta Arithmetica
The dynamical Mertens' theorem describes asymptotics for the growth in the number of closed orbits in a dynamical system. We construct families of ergodic automorphisms of fixed entropy on compact connected groups with a continuum of growth rates on two different growth scales. This shows in particular that the space of all ergodic algebraic dynamical systems modulo the equivalence of shared orbit-growth asymptotics is not countable. In contrast, for the equivalence relation of measurable isomorphism...
Étienne Fouvry (1987)
Annales scientifiques de l'École Normale Supérieure
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