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
https://arxiv.org/abs/2109.04068
Primes as sums of Fibonacci numbers
12.10.2021 16:00 - 17:30
Location:
TU Wien, Zeichensaal 3, Freihaus, Turm A, 7. Stock