Date(s) : 18/10/2022 iCal
11 h 00 min - 12 h 00 min
The purpose of talk is to discuss the relationship between prime numbers and sums of Fibonacci numbers. The main results 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 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