About application of the matrix formalism of the heat kernel to number theory

TL;DR

This paper explores the application of matrix formalism of the heat kernel to number theory, focusing on a simple abelian connection case in 2D to relate operators and generating functions.

Contribution

It extends the matrix formalism of the heat kernel to a specific 2D abelian case, linking operators with generating functions in number theory.

Findings

Controlled coefficients of the heat kernel using matrix formalism

Established relations between operators and generating functions

Provided a mathematical description of operators in the model

Abstract

Earlier in the study of the combinatorial properties of the heat kernel of Laplace operator with covariant derivative diagram technique and matrix formalism were constructed. In particular, this formalism allows you to control the coefficients of the heat kernel, which is useful for calculations. In this paper, a simple case is considered with abelian connection in two-dimensional space. This model allows us to give a mathematical description of operators and find relation between operators and generating functions of numbers.