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Explicit constants in averages involving...
Kim, Sungjin...

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Explicit constants in averages involving the multiplicative order by Kim, Sungjin ( Author )
Lemonjar Open Access
N.A
14-10-2015
Let a>1. Denote by la(p) the multiplicative order of a modulo p. We look for an estimate of sum of la(p)p−1 over primes p≤x on average. When we average over a≤N, we observe a statistic of CLi(x). P. J. Stephens ~\cite[Theorem 1]{S} proved this statistic for N>exp(c1logx−−−−√) for some positive constant c1. Upon this result, we give an explicit value of c1. In fact, ~\cite[Theorem 1, 3]{S} hold with N>exp(3.42logx−−−−√), and ~\cite[Theorem 2, 4]{S} hold with N>exp(4.8365logx−−−−√). Also, we improve the range of y, from y≥exp((2+ϵ)logxloglogx−−−−−−−−−−√) in ~\cite[Theorem 1]{LP}, to y>exp(3.42logx−−−−√).
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https://arxiv.org/abs/1510.04348
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