25 oct 2023 -- 15:00   [open in google calendar]

Aula Dini, Palazzo del Castelletto

Abstract.

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<1211. 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.

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