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Trace and Frobenius Euler Products for a Shifted Divisor Matrix

Year: 2026

Type: preprint

Abstract: For the divisors greater than one of an integer \(a\), this preprint studies a weighted negative inverse of the shifted power GCD matrix. It derives exact Euler-product formulas for the trace of the square and the squared Frobenius norm of the resulting operator. The proof uses a prime-power tridiagonal factorization and computes the distinct row and column corrections caused by deleting the divisor \(1\). The formulas hold for every integer \(a\ge2\) and every positive integer exponent \(k\)

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.24001912

Author: Hau Rava, M

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7225404371

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