Functions and Analysis

1809 Submissions

[3] viXra:1809.0481 [pdf] submitted on 2018-09-24 03:45:57

The Riemann Hypothesis

Authors: Michael Atiyah
Comments: 5 Pages.

The Riemann Hypothesis is a famous unsolved problem dating from 1859. This paper will present a simple proof using a radically new approach. It is based on work of von Neumann (1936), Hirzebruch (1954) and Dirac (1928).
Category: Functions and Analysis

[2] viXra:1809.0234 [pdf] replaced on 2019-08-03 19:27:14

Proof of the Limits of Sine and Cosine at Infinity

Authors: Jonathan W. Tooker
Comments: 48 Pages. Greatly improved v7

We develop a representation of complex numbers separate from the Cartesian and polar representations and define a representing functional for converting between representations. We define the derivative of a function of a complex variable with respect to each representation and then we examine the variation within the definition of the derivative. After studying the transformation law for the variation between representations of complex numbers, we will show that the new representation has special properties which allow for a modification to the transformation law for the variation which preserves, in certain cases, the definition of the derivative. We refute a common proof that the limits of sine and cosine at infinity cannot exist. We use the modified variation in the definition of the derivative to compute the limits of sine and cosine at infinity.
Category: Functions and Analysis

[1] viXra:1809.0171 [pdf] submitted on 2018-09-08 15:03:38

On the Infinite Product for the Ratio of k-th Power and Factorial

Authors: Edigles Guedes
Comments: 3 Pages.

I derive an infinite product for the ratio of k-th power and factorial.
Category: Functions and Analysis