Proof of the Conjencture 5.2 Taken From the Research Paper 'Research Problems in Number Theory'

Authors

  • Amrin Sheikh  Department of Mathematics, Government Vidarbha Institute of Science & Humanities, Amravati, VMV Road, Amravati, Maharashtra, India
  • Mohd Abbas H. Abdy Sayyed  S R Engineering College, Ananthasagar, Hasanparthy, Warangal, Telangana, India

Keywords:

Additive Function, Logarithmic Series, Multiplicative Group

Abstract

The conjecture is taken from the research paper "Research problems in Number Theory" published by Nguyen Cong Hao, Imre K'atai and Bui Minh Phong in the year 2014, that elaborated the concept of additive function, multiplicative function. The conjecture that is proved herein, is deduced for k = 1 from the Wirsing's Theorem that says any real valued multiplicative function/modulus < 1 has a mean value or its limit exists. In this paper, we proved the conjecture 5.2 from the same paper in a simplified way using some basic concepts of arithmetic.

References

  1. Nguyen CH, Imre K and Bui Minh P. (2014). Research Problems in Number Theory. Annales Univ. Sci. Budapest., Sect. Comp. 43: 267-277

International Journal of Scientific Research in Science and Technology

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Published

2018-08-30

Issue

Volume 4, Issue 9, July-August-2018

Section

Research Articles

License

Copyright (c) IJSRST

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
Amrin Sheikh, Mohd Abbas H. Abdy Sayyed, " Proof of the Conjencture 5.2 Taken From the Research Paper 'Research Problems in Number Theory', International Journal of Scientific Research in Science and Technology(IJSRST), Online ISSN : 2395-602X, Print ISSN : 2395-6011, Volume 4, Issue 9, pp.311-313, July-August-2018.