On the Application of the Matrix Formalism for the Heat Kernel to Number Theory
- Authors: Ivanov A.V.1
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Affiliations:
- St. Petersburg Department of Steklov Institute of Mathematics
- Issue: Vol 242, No 5 (2019)
- Pages: 683-691
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/243020
- DOI: https://doi.org/10.1007/s10958-019-04506-4
- ID: 243020
Cite item
Abstract
Earlier, in the study of combinatorial properties of the heat kernel of the Laplace operator with covariant derivative, a diagram technique and matrix formalism were constructed. In particular, the obtained formalism allows one to control the coefficients of the heat kernel, which is useful for calculations. In this paper, we consider a simple case with an Abelian connection in the two-dimensional space. This model allows us to give a mathematical description of the operators and find a relation between these operators and generating functions of numbers.
About the authors
A. V. Ivanov
St. Petersburg Department of Steklov Institute of Mathematics
Author for correspondence.
Email: regul1@mail.ru
Russian Federation, St. Petersburg