Primes as sums of Fibonacci numbers
Lukas Spiegelhofer (Montanuniversität Leoben)
Abstract: We prove that the Zeckendorf sum-of-digits function of prime numbers, $z(p)$, is uniformly distributed in residue classes. The main ingredient that made this proof possible is the study of very sparse arithmetic subsequences of $z(n)$. In other words, we will meet the level of distribution. Our proof of this central result is based on a combination of the "Mauduit−Rivat−van der Corput method" for digital problems and an estimate of a Gowers norm related to $z(n)$. Our method of proof yields examples of substitutive sequences that are orthogonal to the Möbius function (cf. Sarnak's conjecture).
This is joint work with Michael Drmota and Clemens Müllner (TU Wien).
dynamical systemsnumber theory
Audience: researchers in the topic
Series comments: Description: Online seminar on numeration systems and related topics
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| Organizers: | Shigeki Akiyama, Ayreena Bakhtawar, Karma Dajani, Kevin Hare, Hajime Kaneko, Niels Langeveld, Lingmin Liao, Wolfgang Steiner* |
| *contact for this listing |