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Article: The asymptotic formula of [summation over n [less than or equal to] x] log [P.sub.ld](n).
- Article from:
- Scientia Magna
- Article date:
- June 1, 2006
- Author:
CopyrightCOPYRIGHT 2006 American Research Press. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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Abstract Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Where l, q are fixed numbers. This paper uses the hyperbolic summation method and the exponential pair theory to obtain the asymptotic formula of [summation over n[less than or equal to]x] log [P.sub.ld](n).
Keywords Exponential sum, hyperbolic summation method, exponent pair.
[section]1. Introduction
F. Smarandache introduced the function [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] d in Problem 25 of [1]. In this paper we shall define a similar function and study its property. Let 1 [less than or equal to] l [less than or equal to] q be fixed. Now we define a function ...