The level of distribution of the sum-of-digits function in arithmetic progressions

2025/04/03 by N. Toumi, Toumi, Nathan · 1 citation
Mathematics · Computer Science · #Analytic Number Theory Research #Coding theory and cryptography #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.2504.02784

Abstract

For q ≥ 2, n ∈ ℕ, let s_q(n) denote the sum of the digits of n written in base q. Spiegelhofer (2020) proved that the Thue--Morse sequence has level of distribution 1, improving on a former result of Fouvry and Mauduit (1996). In this paper we generalize this result to sequences of type \exp(2πiℓ s_q(n)/b)\_{n ∈ ℕ} and provide an explicit exponent in the upper bound.

Cited by

• Gowers norms for linearly recurrent numeration systems

Related

• The sum of digits function of the base phi expansion of the natural numbers
• The sum of digits of polynomial values in arithmetic progressions
• The level of distribution of the sum-of-digits function of linear recurrence number systems
• Finite generating functions for the sum of digits sequence
• Thue--Morse along the sequence of cubes