4 papers
math.DS2026
The Hydra Map and Numen Formalisms for Collatz-Type Problems
Maxwell C. Siegel
This paper details a generalization of the formalism presented in the author's 2024 paper, "The Collatz Conjecture and Non-Archimedean Spectral Theory - Part I - Arithmetic Dynamic…
math.GM2025
Algebras of -Adic Distributions Induced by Pointwise Products of F-Series
Maxwell C. Siegel
Let be an integer and let be a global field. A foliated -adic F-series is a function of a -adic integer variable satisfying the functional…
math.GM2025
The Collatz Conjecture & Non-Archimedean Spectral Theory -- Part II -- -Adic Fourier Analysis and Wiener's Tauberian Theorem
Maxwell C. Siegel
This paper gives an overview of -adic Fourier theory - the Fourier theory of functions from the -adic numbers to the -adic numbers, where and are di…
math.GM2024
-adic Analysis and the Collatz Conjecture
Maxwell Charles Siegel
What use can there be for a function from the -adic numbers to the -adic numbers, where and are distinct primes? The traditional answer, courtesy of the half-century…