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Generalized prime number theorem and Riemann Hypothesis for non-number math objectsr math r math objects

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Subject: Generalized prime number theorem and Riemann Hypothesis for
non-number math objectsr math r math objects
From: datashap...@gmail.com (Vincent Granville)
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by: Vincent Granville - Mon, 7 Jun 2021 08:02 UTC

My question is about some math objects (matrices, polynomials) and operators that satisfy a number of properties which can lead to a theory similar to PNT, RH, Dirichlet functions, abscissa of convergence, Mertens and related functions, and so on. I am wondering if the framework proposed below has been studied before, and I am looking for references. Also I am looking for interesting examples and whether what I discuss makes sense. The closest I could come up with is the Beurling generalized numbers, Beurling zeta function and PNT for Beurling numbers.

What I propose here is built in the exact same way as Beurling numbers, but involves matrices or functions rather than numbers. The construction is as follows.

Read full article on MathOverflow, at
https://mathoverflow.net/questions/394677/generalized-prime-number-theorem-and-riemann-hypothesis-for-non-number-math-obje

Subject	Author
Generalized prime number theorem and Riemann Hypothesis for	Vincent Granville