D. S. Minenkov, V. E. Nazaikinskii, V. L. Chernyshev, “On the Asymptotics of the Element Counting Function in an Additive Arithmetic Semigroup with Exponential Counting Function of Prime Generators”, Funktsional. Anal. i Prilozhen., 2016, Volume 50, Issue 4,Pages <nobr>55

This article is cited in 8 papers

On the Asymptotics of the Element Counting Function in an Additive Arithmetic Semigroup with Exponential Counting Function of Prime Generators

D. S. Minenkov^ab, V. E. Nazaikinskii^ab, V. L. Chernyshev^c

^a Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia
^b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow Oblast, Russia
^c National Research University Higher School of Economics, Moscow, Russia

Abstract: We find the asymptotics of the element counting function for an additive arithmetic semigroup with exponential growth of the counting function of prime generators.

Keywords: arithmetic semigroup, inverse abstract prime number theorem, counting function, entropy, asymptotics.

UDC: 511.3

Received: 17.12.2015

DOI: 10.4213/faa3256