Arithmetical properties of integer sequences with polynomial growth

Jean-Marc Deshouillers - Institut de Mathématiques de Bordeaux, Université de Bordeaux
Arithmetical properties of integer sequences with polynomial growth

Abstract
In 1933, B. I. Segal introduced the sequences ([n^c])_n - where [x] denotes the integral part of x and c a positive real number which is not an integer - and studied their additive properties. Twenty years later, I. I. PIatetski-Shapiro proved a prime number theorem for those sequences with c<12/11. Those sequences are considered as typical examples of integer sequences with polynomial growth.
In this talk, I shall tackle the question to understand how far those sequences can be considered as “random” sequences of integers as regards their arithmetic properties and illustrate it through results obtained in the last decade.
No special knowledge in number theory is expected from the audience.

The event will take place in person.