Abstract:
Thakur ('04, '09) introduced multiple zeta values associated with the rational function field over a finite field and proved that they are non-zero by using results and arguments of Sheats ('98). In the talk, we show that multiple zeta values associated with function fields of higher genus curves, which were introduced by Lara Rodriguez and Thakur ('21), are non-zero under a certain condition on the Weierstrass gap sequence at a fixed rational point ∞. By the arguments similar to those given by Thakur in his proof for the case of genus zero, we calculate the ∞-adic valuation of a given multiple zeta value explicitly in order to prove the result.
2023-06-28 10:30 ~ 2023-06-28 11:30
Mr. Daichi Matsuzuki (Nagoya University)
Room 723, General Building III