Lecture Room B, 4th Floor, The 3rd General Building, NTHU

(清華大學綜合三館 4樓B演講室)

Alternating Multizeta Values in Characteristic p

Ryotaro Harada (Nagoya University)

Abstract:

In 2004, D. S. Thakur invented the positive characteristic analogue of multizeta values (MZVs in short) which are higher depth generalizations of Carlitz zeta values.

By the work of Anderson and Thakur, it is known that MZVs are non-trivial values which have an algebra structure and are periods of certain t-motive. Later on, in 2014, C.-Y. Chang proved that there do not exist nontrivial linear relations among MZVs with different weight.

In this talk, we introduce generalizations of MZVs which we call alternating multizeta values in positive characteristic. Moreover, we show that they also satisfy fundamental properties including non-vanishing, sum-shuffle, period interpretation and linear independence as alternating analogues of the results given by Anderson-Thakur (2009), Chang (2014) and Thakur (2009, 2010).