Fonctionne avec Indico
v3.2.9
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