What question did this study set out to answer?

The aim is to present a new operator-theoretic framework for Artin L-functions linked to Euler's totient function.

January 16, 20260 citationsOpen Access

The φ(n)-Residue Framework for L-Functions: A Constructive Spectral Approach to the Riemann Hypothesis

Key Points

The aim is to present a new operator-theoretic framework for Artin L-functions linked to Euler's totient function.
Introduces a constructive spectral approach to Artin L-functions.
Utilizes a multiplicative boundary condition derived from Euler’s totient function.
Provides an exposition on boundary conditions, dilation symmetry, and curvature estimates.
Establishes a connection to zero distributions under explicit analytic hypotheses.
Highlights the significance of the φ(n)-residue boundary and spectral wall inequality.

Abstract

This preprint introduces an operator-theoretic framework for Artin L-functions based on a multiplicative boundary condition arising from Euler’s totient function. The construction is unconditional; the connection to zero distributions requires explicit analytic hypotheses. A full exposition, including the φ(n)-residue boundary, dilation symmetry, curvature estimates, and the spectral wall inequality, is provided.

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Trent Palelei (Thu,) studied this question.

synapsesocial.com/papers/6969d4dc940543b977709c11 https://doi.org/https://doi.org/10.5281/zenodo.18250435

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