Dissertation > Excellent graduate degree dissertation topics show

Arithmetical functions mean estimates and Smarandache

Author: LiuYanNi
Tutor: ZhangWenPeng
School: Northwestern University
Course: Basic mathematics
Keywords: Smarandache functions Arithmetic functions Asymptotic formula Mean value Pseudo number sequence Infinity series
CLC: O156.4
Type: Master's thesis
Year: 2007
Downloads: 46
Quote: 0
Read: Download Dissertation

Abstract


It is well known that the mean value problems of arithmetical functions play an important role in the study of analytic number theory, and they relate to many famous number theoretic problems. Therefore, any nontrivial progress in this field will contribute to the development of analytic number theory. American-Romanian number theorist Florentin Smarandache introduced hundreds of interesting sequences and arithmetical functions, and presented many problems and conjectures in his life. In 1991, he published a book named "Only problems, Not solutions!" . He presented 105 unsolved arithmetical problems and conjectures about these functions and sequences in it. Many researchers studied these sequences and functions from this book, and obtained important results.In this dissertation, we study the mean value problems of some important arithmetical functions and some aspect about Smarandache unsolved problems. The main achievements contained in this dissertation are as follows:1. The mean value problems of some functions are studied. We study the properties of this sequence e_p(n) and give some asymptotic formulas while e_p(n) denoted the largest exponent of power p which divides n. We introduce two new arithmetical functions P_d(n) and f(n), and give two interesting asymptotic formula.2. Smarandache function S(n) has very important position in the study of number theory. We use the elementary methods to study the solutions of some equations involving the Smarandache function.3. We study the mean value properties of the second Smarandache pseudo-odd number sequence and pseudo-even number sequence, and give some interesting asymptotic formulae for them.4. Studying some infinity series is very significant. We use the elementary method to study the convergent properties of this simple infinity series, and give some interesting identity.

Related Dissertations

  1. A Vector Map Digital Watermarking Algorithm Based on N-point Mean Value,TP309.7
  2. Mean Value Formula and Integer Point Problem for Some Number Theory Functions,O156.4
  3. Research on Modal Analysis and Its Application of Stochastic Parameter Structure,TH113.1
  4. Modeling and Simulation of Large-Scale Low-Speed Marine Diesel Engine,U664.121
  5. A Generalization of Bombieri-Vinogradov Type Theorem,O156.4
  6. Estimates for Certain Types of Character Sums,O156.4
  7. Mean Value of the Square Root Sequence and Arithmetical Function U(n),O156.4
  8. The K-th Power Sum Functions of GCD and LCM,O156.4
  9. The Establishment and Experimental Investigation of Mean Value Engine Model of Gasoline Engine,TK417
  10. Research on the related issues of the several F.Smarandache number theoretic function,O156.4
  11. About some of the Smarandache series with the mean estimate number theoretic function,O156.4
  12. Research on Square Free Numbers and Smarandache Functions,O156.1
  13. A Study on the Mean Value of Some Famous Summations in Number Theory,O156.4
  14. Primary Study on Spatial Powers Combining of High Power Microwave,TN73
  15. Mean-square Value of the Error Term on Three-dimensional Divisor Problem of (a, a, b) Type,O156
  16. The mean estimate of arithmetical functions and equation solving arithmetical functions,O156.4
  17. Research on Some Color Transfering Problems,O175.2
  18. Globally Asymptotical Stability of High-order Delay Hopfield Neural Networks,TP183
  19. On Proportionality of Risk Premium Calculation Principles and the Problems of Cooperation Insurance,F840
  20. The Geometric Mean Value of Product of Non-zero Digits in Base 10 and the Mean Value of Some Number Functions for Square Complements,O156

CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Number Theory > Analytic Number Theory
© 2012 www.DissertationTopic.Net  Mobile