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

Earlier, in the studies of the combinatorial properties of the heat kernel of Laplace operator with covariant derivative, the diagram technique and the matrix formalism were constructed. In particular, the obtained formalism makes it possible to control the coefficients of the heat kernel, that is rather useful for calculations. In this paper, a simple case with abelian connection in two-dimensional space is considered. We give a mathematical description of operators and find a relation between operators and generating functions of numbers.