Symmetric multiple zeta functions
Year: 2025
Type: article
Abstract: In this study, we introduce multiple zeta functions with structures similar to those of symmetric functions such as the Schur P-, Schur Q-, symplectic and orthogonal functions in representation theory. Their basic properties, such as the domain of absolute convergence, are first considered. Then, by restricting ourselves to the truncated multiple zeta functions, we derive the Pfaffian expression of the Schur Q-multiple zeta functions, the sum formula for Schur P- and Schur Q-multiple zeta functions, the determinant expressions of symplectic and orthogonal Schur multiple zeta functions by making an assumption on variables. Finally, we generalize those to the quasi-symmetric functions.
Source: Canadian Journal of Mathematics
Authors: Maki Nakasuji, Wataru Takeda
Institutions: Tohoku University, Sophia University, Toho University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4408800266