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Mahler measure, integral

K_{2}

and Beilinson's conjecture of curves over number fields

组织者

盛茂 , 阿尔坦·谢什马尼 , 杨南君 , 袁北彗

演讲者

Guoping Tang

时间

2023年11月09日 15:30 至 17:00

地点

YMSC-Jingzhai-304

线上

Zoom 638 227 8222 (BIMSA)

摘要

We will talk about several Mahler measure identities involving families of two-variable polynomials defining curves of arbitrary genus, by means of their integral

K_{2}

. As an application, we can obtain some relations between the Mahler measure of non-tempered polynomials defining elliptic curves of conductor 14, 15, 24, 48, 54 and corresponding L-values. We construct

g

independent (integral) elements in the kernel of the tame symbol on several families of curves with genus

g = 1, 2, 4, 7

. Furthermore, we prove that there exist non-torsion divisors

P - Q

with

P, Q

in the divisorial support of these

K_{2}

elements when

g = 1, 2

, which is potentially different from previous constructions in literature.