Pseudo-differential Operators on the Circle, Bernoulli Polynomials

Authors

Roger Gay, University Bordeaux
Ahmed Sebbar, Chapman UniversityFollow

Document Type

Article

Publication Date

2-17-2024

Abstract

We show how the classical polylogarithm function Li_s (z) and its relatives, the Hurwitz zeta function and the Lerch function are all of a spectral nature, and can explain many properties of the complex powers of the Laplacian on the circle and of the distribution (x +i0)^s .We also make a relation with a result of Keiper [Fractional Calculus and its relationship to Riemann’s zeta function, Master of Science, Ohio State University, Mathematics (1975)].

Comments

This article was originally published in Quantum Studies: Mathematics and Foundations in 2024. https://doi.org/10.1007/s40509-024-00316-9

Recommended Citation

Gay, R., Sebbar, A. Pseudo-differential operators on the circle, Bernoulli polynomials. Quantum Stud.: Math. Found. (2024). https://doi.org/10.1007/s40509-024-00316-9

Peer Reviewed

1

Copyright

The authors

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.