We introduce the nonvanishing results on some Hecke L-functions. In the first talk, we recall basic definitions including the Hecke character, its L-function, and global/local root number. Also, some well-known theories related to our motivation including the Birch—Swinnerton-Dyer conjecture, and complex multiplication theory will be mentioned.

In the second talk, we review Yang’s result which interprets the special L-values of the Hecke L-function via theta lifting. After that, we give some local computations, which allow us to give a nonvanishing of L-functions of some hyperelliptic curves and Fermat curves. This talk is based on the papers collaborated with Junyeong Park, Yeong-Wook Kwon, and Donggeon Yhee.


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Meeting ID: 665 424 7590

Passcode: dynamics