On irregularities of distribution of binary sequences relative to arithmetic progressions, I. (General results)

Cécile Dartyge (1) , Katalin Gyarmati (2, 3) , András Sárközy (3)

1 IECL - Institut Élie Cartan de Lorraine
2 MTA - Hungarian Academy of Sciences
3 Department of Algebra and Number Theory [Budapest]

In 1964 K. F. Roth initiated the study of irregularities of distribution of binary sequences relative to arithmetic progressions and since that numerous papers have been written on this subject. In the applications one needs binary sequences which are well distributed relative to arithmetic progressions, in particular, in cryptography one needs binary sequences whose short subsequences are also well-distributed relative to arithmetic progressions. Thus we introduce weighted measures of pseudorandomness of binary sequences to study this property. We study the typical and minimal values of this measure for binary sequences of a given lenght

Mots clés: binary sequence; well-distribution; arithmetic progressions

Domaines: Théorie des nombres [math.NT]

Cécile Dartyge, Katalin Gyarmati, András Sárközy. On irregularities of distribution of binary sequences relative to arithmetic progressions, I. (General results). Uniform Distribution Theory, 2017, 12 (1), pp.55-67. ⟨10.1515/udt-2017–0004⟩. ⟨hal-01280840⟩