A Stronger Generalization of the Riemann Functional Equation

A major breakthrough introduced in this paper is a generalization of the Riemann functional equation that has a broader validity domain than the existing one from the literature. The insight that led to this new relation came from a new formula for the zeta function created herein that implies the Riemann functional equation. Further developments that stem from new formulae introduced previously are also discussed. Btw, someone has pointed out that there is an easier solution, in hindsight, that can be used to derive this generalization. Typical nay-sayism. It only matters if someone has used that same logic to come up with the formula before it was published! The new formula can also be dissmissed as deja-vu if the result already existed previously in the literature, but in no other case. Coming up with easier ways to deduce a formula (which relies on the formula itself after it's known) is not how problems are solved. You only got the insight because you saw the look and feel of the new result.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-06-18
DOI
https://doi.org/10.5281/zenodo.15707461
Primary Topic
Veterinary Oncology Research
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

A Stronger Generalization of the Riemann Functional Equation

Zenodo (CERN European Organization for Nuclear Research)
Veterinary Oncology Research
article

A Stronger Generalization of the Riemann Functional Equation

article en

Abstract

A major breakthrough introduced in this paper is a generalization of the Riemann functional equation that has a broader validity domain than the existing one from the literature. The insight that led to this new relation came from a new formula for the zeta function created herein that implies the Riemann functional equation. Further developments that stem from new formulae introduced previously are also discussed. Btw, someone has pointed out that there is an easier solution, in hindsight, that can be used to derive this generalization. Typical nay-sayism. It only matters if someone has used that same logic to come up with the formula before it was published! The new formula can also be dissmissed as deja-vu if the result already existed previously in the literature, but in no other case. Coming up with easier ways to deduce a formula (which relies on the formula itself after it's known) is not how problems are solved. You only got the insight because you saw the look and feel of the new result.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 37%
Veterinary Oncology Research
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.