Abstract
In this expository note we use uniform distribution to clarify a result on the difference of an element and its inverse in (Z/nZ)*. We then explain why our remarks apply to some other settings. In doing so we state and prove a couple of folklore theorems on uniform distribution.
Similar content being viewed by others
REFERENCES
B. C. BERNDT, R. J. EVANS and K. S. WILLIAMS, Gauss and Jacobi Sums, John Wiley & Sons, 1998.
E. BOMBIERI, On Exponential Sums in Finite Fields, Amer. J. Math. 88 (1966), 71–105.
S. CHOWLA, On Kloostermanss's Sum, Norske Vid. Selbsk. Fak. Frondheim 40 (1967), 70–72.
R. M. CORLESS, Essential Maple: an introduction for scientific programmers, Springer-Verlag, 1995.
J. H. H. CHALK and R. A. SMITH, On Bombieri's estimate for exponential sums. Acta Arith. 18 (1971), 191–212.
H. DAVENPORT, On certain exponential sums, The Collected Works of Harold Davenport, Vol. IV, Academic Press, 1977, 1462–1480; (This paper first appeared in Journal fűr Math. 169 (1933), 158–176.)
M. DROMOTA and R. F. TICHY,Sequences, Discrepancies and Applications, Lect. Notes in Math., vol. 1651, Springer-Verlag, 1997.
T. ESTERMANN, On Kloosterman's Sum, Mathematika 8 (1961), 83–86.
G. H. HARDY and E. M. WRIGHT, An Introduction to the Theory of Numbers, (5th edn), Oxford University Press, 1979.
L. K. HUA, Introduction to Number Theory, translated from the Chinese by P. Shiu, Springer-Verlag, 1982.
W. M. SCHMIDT, Equations over finite fields-An elementary approach, Lect. Notes in Math., vol, 536, Springer-Verlag, Berlin, 1976.
A. WEIL, Sur les courbes algébriques et les varieties qui s'en déduisent, Actualités sci. et ind. 1041, (1948).
A. WEIL, On some exponential sums, Proc. Nat. Acad. Sci., 34 (1948), 204–207.
ZHANG WENPENG, On the Distribution of Inverses Modulo n, J. Number Theory 61 (1996), 301–310.
WENPENG ZHANG, On the Distribution of Primitive Roots Modulo p, Publ. Math. Debrecen 53 (1998), 245–255.
ZHIYONG ZHENG, The Distribution of Zeros of an Irreducible Curve over a Finite Field, J. Number Theory 59 (1996), 106–118.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Beck, J., Khan, M.R. On the Uniform Distribution of Inverses modulo n. Periodica Mathematica Hungarica 44, 147–155 (2002). https://doi.org/10.1023/A:1019684111647
Issue Date:
DOI: https://doi.org/10.1023/A:1019684111647