Number theory: primes, arithmetic functions, modular computations, special sequences

An interactive for visualizing complex functions based on a 3Blue1Brown video and also estimation of Riemann Zeta Function using Euler Maclaurin Summation.

This repository contains an MPI program written in C that calculates the Riemann zeta function and evaluates its performance using MPI collective communication functions. The program approximates the value of ζ(3) with a given value of `s` (3 - Apéry's constant). It calculates the runtime, speedup, and efficiency for different numbers of processes.

This is my repo of various prime number plots and experiments.

Official repo for Modular Substrate Theory (MST). Geometric unification of Cosmology & Hadronic Spectroscopy from first principles. Resolves H₀/S₈ tensions, predicts exotic states (d**), and validates vacuum structure via prime number spectral resonance. Zero free parameters.

Modular Spectrum of Pi: reference implementation of the Stride-6 engine. Unifies Chudnovsky's series with DSP polyphase decomposition in Z/6Z. Validated at 100M digits with 95% parallel efficiency. Features a Shared-Nothing architecture to bypass the memory wall and maximize cache alignment.

Official repo for the paper: "The Emergence of Geometry". Analytical derivation and 150-digit validation of the identity linking ζ(0), ln 2, and the emergence of spatial geometry within the Z/6Z modular substrate.

This repository contains a modular Python toolkit for studying the Riemann-Zeta function on the critical line and certifying its non-trivial zeros.

D-ND Framework — Research papers on the Dual-Non-Dual mathematical structure bridging number theory, quantum mechanics, and information geometry

Fortran, MATLAB and Python code for computing Riemann zeta and log Gamma functions (and their derivatives) in the complex plane

Sieving primes and counting primes

First 2,001,052 zeros of zeta function

nfield: A structural analysis engine for the collision invariant of the digit function, connecting long division to L-function special values. Source code, publications, and companion research notes.

This repository contains investigations of the distribution of Riemann zeta zeros, with machine learning applications and study of symmetry properties

Educational game about the Riemann Zeta function. Now officially published.

Computational framework for emergent coherent integration in adaptive multi-agent systems