Abstract
We prove that any set of integers A ⊂ [1, x] with |A| ≫ (logx)r lies in at least va(p) ≫ pr/r+1 many residue classes modulo most primes p ≪ (log x)r+1. (Here r 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 x which are multiplicatively generated by the coprime integers a1,..., ar (i.e. whose counting function is also c(log x)r) lie in at least pr/r+1+ε(p) residue classes, modulo most small primes p, where ε(p) → O, as p→ ∞.
Originalsprache | englisch |
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Seiten (von - bis) | 2247-2250 |
Seitenumfang | 4 |
Fachzeitschrift | Proceedings of the American Mathematical Society |
Jahrgang | 130 |
Ausgabenummer | 8 |
DOIs | |
Publikationsstatus | Veröffentlicht - Aug. 2002 |
ASJC Scopus subject areas
- Mathematik (insg.)
- Angewandte Mathematik