Number Theory

2610 Submissions

[3] viXra:2610.0037 [pdf] submitted on 2026-10-10 00:48:07

Note to Analytical Derivation of Viswanath's Constant

Authors: Miroslav Súkeník, Magdaléna Súkeníková
Comments: 3 Pages.

In the article, we examine the control functions that enable the analytical derivation of Viswanath's constant.
Category: Number Theory

[2] viXra:2610.0020 [pdf] submitted on 2026-10-06 00:35:46

A Rigorous Proof of the Riemann Hypothesis via Geometric Characterization of the Dirichlet Eta Function: Half-Angle Residual Dynamics and Invariant Level-Crossing Barriers ```[span_0](start_span)[span_0](end_span)

Authors: Ali Rıza Şahin
Comments: 13 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper establishes a rigorous real-analytic and geometric framework governing the distribution of the non-trivial zeros of the Dirichlet eta function $eta(s)$ across the critical strip $mathcal{S}={sinmathbb{C}:00$ simultaneously across dual orthogonal projections with an exact $pi/4$ phase shift. We establish that this simultaneous locking condition enforces an overdetermined phase alignment and a structural polarization disparity between the dual channels, providing an absolute real-variable obstruction that strictly confines all non-trivial zeros to the critical line $mathbb{R}(s)=1/2$. By demonstrating that this geometric barrier is mathematically insurmountable, this work establishes a rigorous and definitive proof of the Riemann Hypothesis.
Category: Number Theory

[1] viXra:2610.0007 [pdf] submitted on 2026-10-02 12:49:36

A Sum of Three Squares in Which One is the Product of the Other Two

Authors: Walter A. Kehowski
Comments: 10 Pages.

The identity x^2 + (x+1)^2 + (x(x+1))^2 = (x^2+x+1)^2 is the motivation for study of the equation d^2 + e^2 + n^2 = x^2, where d and e are conjugate divisors of n, that is, n=de and $d1 fall empirically into two families: a triangular family mathscr{T}, and a Fibonacci family mathscr{F}, with virtually no overlap. It is conjectured that the two families comprise all n with |N_{n}|>1.
Category: Number Theory