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Mahler measure, integral $K_2$ and Beilinson's conjecture of curves over number fields

来源: 11-09

时间:2023-11-09 Thu 15:30-17:00

地点:YMSC-Jingzhai-304 ZOOM: 638 227 8222(PW: BIMSA)

组织者:Mao Sheng, Nanjun Yang

主讲人:Guoping Tang

Abstract

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.

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