Functions and Analysis

1912 Submissions

[4] viXra:1912.0198 [pdf] replaced on 2019-12-12 06:30:27

The Kakeya Set Conjecture is Valid

Authors: Johan Aspegren
Comments: 5 Pages.

In this paper we will prove the Kakeya set conjecture. Secondly, we build a direct connection between line incidence theorems and Kakeya type conjectures.
Category: Functions and Analysis

[3] viXra:1912.0182 [pdf] submitted on 2019-12-09 09:59:19

Series and Functions

Authors: Viola Maria Grazia
Comments: 1 Page.

I talk about functions in particular I speak when the serie diverges and so when a function tends to infinity.
Category: Functions and Analysis

[2] viXra:1912.0123 [pdf] submitted on 2019-12-06 17:40:20

Refutation of the Fan Theorem

Authors: Colin James III
Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Note that Disqus comments here are not read by the author; reply by email only to: info@cec-services dot com. Include a list publications for veracity. Updated abstract at ersatz-systems.com.

The definition of the decidable fan theorem is evaluated as not tautologous, hence refuting it and derived conjectures such as “uniform continuity theorem with continuous moduli”. These results form a non tautologous fragment of the universal logic VŁ4.
Category: Functions and Analysis

[1] viXra:1912.0030 [pdf] submitted on 2019-12-02 11:50:41

Zeros of the Riemann Zeta Function Within the Critical Strip and Off the Critical Line

Authors: Jonathan W. Tooker
Comments: 22 Pages. 1 color figure

In a recent paper, the author demonstrated the existence of real numbers in the neighborhood of infinity. It was shown that the Riemann zeta function has non-trivial zeros in the neighborhood of infinity but none of those zeros lie within the critical strip. While the Riemann hypothesis only asks about non-trivial zeros off the critical line, it is also an open question of interest whether or not there are any zeros off the critical line yet still within the critical strip. In this paper, we show that the Riemann zeta function does have non-trivial zeros of this variety. The method used to prove the main theorem is only the ordinary analysis of holomorphic functions. After giving a brief review of numbers in the neighborhood of infinity, we use Robinson's non-standard analysis and Eulerian infinitesimal analysis to examine the behavior of zeta on an infinitesimal neighborhood of the north pole of the Riemann sphere. After developing the most relevant features via infinitesimal analysis, we will proceed to prove the main result via standard analysis on the Cartesian complex plane without reference to infinitesimals.
Category: Functions and Analysis