The distribution of sequences in residue classes

Author:
Christian Elsholtz

Journal:
Proc. Amer. Math. Soc. **130** (2002), 2247-2250

MSC (1991):
Primary 11N69, 11N36; Secondary 11B50, 11A07

DOI:
https://doi.org/10.1090/S0002-9939-02-06395-5

Published electronically:
January 23, 2002

MathSciNet review:
1896404

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Abstract: We prove that any set of integers with lies in at least many residue classes modulo most primes . (Here is a positive constant.) This generalizes a result of Erdos and Ram Murty, who proved in connection with Artin's conjecture on primitive roots that the integers below which are multiplicatively generated by the coprime integers (i.e. whose counting function is also ) lie in at least residue classes, modulo most small primes , where as .

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Additional Information

**Christian Elsholtz**

Affiliation:
Institut für Mathematik, Technische Universität Clausthal, Erzstrasse 1, D-38678 Clausthal-Zellerfeld, Germany

Email:
elsholtz@math.tu-clausthal.de

DOI:
https://doi.org/10.1090/S0002-9939-02-06395-5

Keywords:
Distribution of sequences in residue classes,
Gallagher's larger sieve,
primitive roots,
Artin's conjecture

Received by editor(s):
March 9, 2001

Published electronically:
January 23, 2002

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 2002
American Mathematical Society