Work

Exact Gram Inversion for Fractional-Part Approximation

Year: 2026

Type: preprint

Abstract: Exact finite Gram inversion, ordinary sawtooth least-squares errors and rigorous reciprocal-dilate certificates. The Riemann hypothesis and the limiting reciprocal approximation criterion remain unproved. We solve the finite least-squares problem for ordinary sawtooth dilates by explicit Gram inversion and obtain its exact error and asymptotic constant. For the distinct reciprocal-dilate problem, we derive rational Gram certificates, rigorous residual intervals and Hardy-space zero bounds. The Riemann hypothesis remains open.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.24054093

Authors: Bhattacharjee, Deep, Nandi, Pallab, Frederick, Onwuka, Samal, Priyanka

Institutions: Indian Institute of Science Education and Research Kolkata, Ekiti State University

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7225569676

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