On one number-theoretic conception: towards a new theory
Abstract
In this paper we present a new mathematical conception based on a new method for ordering the integers. The method relies on the assumption that negative numbers are beyond infinity, which goes back to Wallis and Euler. We also present a new axiom system, the model of which is arithmetics. We define regular method for summation of infinite series which allows us to discover general and unified approach to summation of divergent series, and determine the limits of unbounded and oscillating functions. Several properties for divergent series and explicit formulas for sums of some infinite series are established. A number of finite and new recurrence formulas for Bernoulli numbers are obtained. We rederive some known results, but in a simpler and elementary way, and establish new results by means of techniques of the theoretical background developed.
Keywords
Cite
@article{arxiv.0907.1090,
title = {On one number-theoretic conception: towards a new theory},
author = {Rom Varshamov and Armen Bagdasaryan},
journal= {arXiv preprint arXiv:0907.1090},
year = {2009}
}
Comments
54 pages; the paper reorganized, divided into paragraphs, cross-refs included, and new references added