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About Smarandache function in some special sequence of lower bounds and related issues

Author: SuJuanLi
Tutor: ZhangWenPeng
School: Northwestern University
Course: Basic mathematics
Keywords: Lower bound estimate Asymptotic formula Smarandache LCM function dual function Mean square value Smarandache k th power screening method
CLC: O156.4
Type: Master's thesis
Year: 2010
Downloads: 22
Quote: 0
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Abstract


As we all know , on some special sequences and properties of arithmetic functions has been studied in number theory occupies a very important position, many famous number theory problems are closely related . Therefore in this area are bound to make any substantial progress on elementary number theory and analytic number theory play an important role in promoting the development of the famous American professor of Romanian mathematician Florentin Smarandache in its publication entitled \problems and conjecture, but also in Japan , Dr. Kenichiro Kashihara \a more in-depth research, and get a lot of important theoretical results. based on the above of interest , using elementary methods and analytical methods on a number of related issues, got some good results , the specific content and achievements divided into the following three aspects: 1. using elementary studied Smarandache function in some special sequence lower bound on the problem , got some strong lower bound estimate .2 using elementary methods, analytical methods, and distribution of prime numbers theorem, SmarandacheLCM function with its dual function mean square value of the distribution problem, give these two functions mean square value of a strong asymptotic formula , these two functions to get some interesting properties of the mean distribution .3 . defines a kinds of new Smarandache k th power screening method , using the elementary method of screening series , we obtain an interesting asymptotic formula .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Number Theory > Analytic Number Theory
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