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On the Distribution of Inverses Modulon

✍ Scribed by Zhang Wenpeng

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 332 KB
Volume: 61
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1996.0151

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✦ Synopsis

Let n>2 be an integer, and for each integer 0<a<n with (a, n)=1, define aÄ by the congruence aaÄ #1 (mod n) and 0<aÄ <n. The main purpose of this paper is to study the distribution behaviour of |a&aÄ |, and prove that for any fixed positive number 0<$ 1,

where ,(n) is the Euler function, and *[ } } } ] denotes the number of elements of the set

In this paper, we shall solve this problem, and give a sharp asymptotic formula. The constants implied by the O-symbols and the symbols R used in this paper do not depend on any parameter, unless otherwise indicated. By using estimates for Kloostermann sums and trigonometric sums, we prove the following: article no.

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