Moments of a Thue-Morse generating function

Hugh L. Montgomery (1) , Christian Mauduit (2, 3) , Joel Rivat (2)

1 Department of Mathematics - University of Michigan
2 I2M - Institut de Mathématiques de Marseille
3 IUF - Institut universitaire de France

We study the moments of even order of the generating function of the Thue-Morse sequence and present several conjectures related to these moments.

Mots clés: Thue-Morse sequence; prime numbers; digits; sum; Prouhet–Thue–Morse sequence; Cayley–Hamilton theorem; combinatorial identity

Domaines: Théorie des nombres [math.NT]

Hugh L. Montgomery, Christian Mauduit, Joel Rivat. Moments of a Thue-Morse generating function. Journal d'analyse mathématique, 2018, 135 (2), pp.713-724. ⟨10.1007/s11854-018-0050-y⟩. ⟨hal-01272983⟩