Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-04-30T21:54:30.114Z Has data issue: false hasContentIssue false
  • English
  • Français

The order of inverses mod q

Part of: Multiplicative number theory

Published online by Cambridge University Press:  26 February 2010

Cristian Cobeli  and
Alexandru Zaharescu
Cristian Cobeli
Affiliation:
Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700 Bucharest, Romania.
Alexandru Zaharescu
Affiliation:
Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700 Bucharest, Romania.
Get access

Abstract

Let q be a prime number and let a = (a1, …, as) be an s-tuple of distinct integers modulo q. For any x coprime with q, let be such that . For fixed s and q→∞ an asymptotic formula is given for the number of residue classes x modulo q for which

The more general case, when q is not necessarily prime and x is restricted to lie in a given subinterval of [1, q], is also treated.

MSC classification

Secondary: 11N69: Distribution of integers in special residue classes
Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000 , pp. 87 - 108
Copyright
Copyright © University College London 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bombieri, E.. On exponential sums in finite fields. Amer. J. Math., 88 (1966), 71–105.CrossRefGoogle Scholar
2.Davenport, H.. On a principle of Lipschitz. J. London Math. Soc., 26 (1951), 179–183.Google Scholar
3.Esterman, T.. On Kloosterman's sums. Mathematika, 8 (1961), 83–86.Google Scholar
4.Hardy, G. H. and Wright, E. M.. An Introduction to the Theory of Numbers, Clarendon Press (Oxford, 1938) (fourth edition 1960).Google Scholar
5.Hooley, C.. On the intervals between consecutive terms of sequences. Proc. Symp. Pure Math., 24 (1973), 129–140.CrossRefGoogle Scholar
6.Moreno, C. J. and Moreno, O.. Exponential sums and Goppa codes. Proc. Amer. Math. Soc., 111 (1991), 523–531.Google Scholar
7.Weil, A.. On some exponential sums. Proc. N.A.S., 34 (1948), 204–207.Google Scholar