Some theorems on multiplicative orders modulo p on average

JOURNAL OF NUMBER THEORY

卷:208

Article

Kim, Sungjin¹ 

[1] Calif State Univ Northridge, Santa Monica Coll, Northridge, CA 91330 USA

关键词: Multiplicative order;    Modulo p;    Average;    Central limit theorem;    Divisor function;   

DOI  :  10.1016/j.jnt.2019.07.024

来源: Elsevier

【 摘 要 】

Let p be a prime, a >= 1, and l(a)(p) be the multiplicative order of a modulo p. We prove various theorems concerning the averages of l(a) (p) over p <= x and a <= y. We prove that these theorems hold for y > exp((alpha+epsilon) root log x) where alpha approximate to 3.42. This is an improvement over y > exp(c(1))root logx) with c(1) >= 12e(9) given in [S2]. We also provide the average of tau(l(a)(p)) over p <= x, a <= y, and y > exp((alpha + epsilon) root log x), where tau(n) is the divisor function Sigma(d/n)1. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free