Gowers norms for linearly recurrent numeration systems

Abstract

Gowers norms have been a key component in the proofs of many breakthrough results in connection to the sum of digits function. Spiegelhofer has used them to show that the Thue-Morse sequence has level of distribution 1 and also that it is equidistributed along cubes. Recently Gowers norms have been used to study the sum of digits function of the Zeckendorf expansion of primes. In this paper we unify the treatments of Gowers norms and give Gowers norms type estimates for a large class of linearly recurrent numeration systems.