Abstract
We present a new “integral (Formula presented.) series” type identity of multiple zeta values, and show that this is equivalent in a suitable sense to the fundamental theorem of regularization. We conjecture that this identity is enough to describe all linear relations of multiple zeta values over (Formula presented.). We also establish the regularization theorem for multiple zeta-star values, which too is equivalent to our new identity. A connection to Kawashima’s relation is discussed as well.
| Original language | English |
|---|---|
| Pages (from-to) | 1-23 |
| Number of pages | 23 |
| Journal | Selecta Mathematica, New Series |
| DOIs | |
| Publication status | Accepted/In press - 2018 Feb 16 |
Keywords
- Kawashima’s relation
- Multiple zeta values
- Multiple zeta-star values
- Regularized double shuffle relation
ASJC Scopus subject areas
- Mathematics(all)
- Physics and Astronomy(all)
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Kaneko, M., & Yamamoto, S. (Accepted/In press). A new integral–series identity of multiple zeta values and regularizations. Selecta Mathematica, New Series, 1-23. https://doi.org/10.1007/s00029-018-0400-8