## Colloquium de l'IDP

**Primes as sums of Fibonacci numbers**

Michael Drmota (TU Wien)

Thursday 17 March 2022 14:00 - Tours -

**Résumé :**

The purpose of the talk is to discuss the relationship between prime numbers and sums of Fibonacci numbers. The main result says that for every sufficiently large integer k there exists a prime number that can be represented as the sum of k different and non-consecutive Fibonacci numbers. This property is closely related to, and based on, a prime number theorem for certain so-called morphic sequences. The proof uses Gowers norms estimates that leads to level-of-distribution results as well as to estimates of sums of type I and II. Furthermore a strong central limit theorem for the Zeckendorf sum-of-digits function along primes has to be established.

This is joint work with Clemens Müllner and Lukas Spiegelhofer

https://arxiv.org/abs/2109.04068

**Liens :**