The arithmetic folding operator on a family of L-functions
Year: 2026
Type: preprint
Abstract: The finite difference of a prime sum cancels the main term and leaves frequencies at the ordinates of zeros of an L-function. A previous note treated only the Riemann zeta function. This paper applies the same difference to Dirichlet characters, to an elliptic curve, to a contrast of two scales, and to residue classes of primes. On sixteen primitive real characters of conductors 3 to 29, every character at 20000 primes is detected at score z greater than 3, and the median frequency error stays a constant fraction of the Hann bin (mean ratio 0.182, so C_res about 1.14). The algebraic bookkeeping was checked in Lean 4. The truncation bound is the classical explicit formula and does not use the Riemann hypothesis. A partial Euler product over one residue class has the line Re(s)=0 as a natural boundary. Detection rates are numerical. This is not a competitive zero finder. The record contains the English version (main file), a faithful Portuguese version, and a supplementary archive with the verification script, figures, the conductor table, and the Lean 4 files checked with AXLE. Second paper of a pair. It extends doi:10.5281/zenodo.24034658, which treated only the zeta function.
Author: de Melo, Fábio Dayan Soares
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225593766