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NCTS Seminar on Number Theory
 
13:30 - 14:30, January 6, 2021 (Wednesday)
broadcast in Lecture Room B, 4th Floor, The 3rd General Building, NTHU, Online seminar
(線上演講 於清大綜合三館Lecture Room B收播)
Genus Character L-functions of Quadratic Orders and Class Number Formulas
Masanobu Kaneko (Kyushu University)

Abstract:

For any quadratic orders, we explicitly calculate the genus character L-functions in full generality.  This generalizes our old computation related to the Chowla-Selberg formula for non-fundamental orders.    
As an application, we generalize a formula due to Hirzebruch-Zagier which expresses the class numbers of some imaginary quadratic fields in terms of continued fraction expansions of suitable quadratic numbers. This is a joint work with Yoshinori Mizuno.
 
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