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# Communications in Number Theory and Physics

## Volume 9 (2015)

### Number 4

### A note on the algebra of $p$-adic multi-zeta values

Pages: 689 – 705

DOI: http://dx.doi.org/10.4310/CNTP.2015.v9.n4.a2

#### Author

#### Abstract

We prove that the algebra of $p$-adic multi-zeta values, as defined in [4] or [2], are contained in another algebra which is defined explicitly in terms of series. The main idea is to truncate certain series, expand them in terms of series all of which are divergent except one, and then take the limit of the convergent one. The main result is Theorem 3.12.