NTS ABSTRACTSpring2025

Back to the number theory seminar main webpage: Main page

Jan 30

L-values and the Mahler measures of polynomials

Xuejun Guo (Nanjing University)

When the zero locus of a tempered polynomial f(x,y) defines an elliptic curve E, the  value L(E,2) is related to the Mahler measure of  f(x,y). In this talk,  we will explore explicit identities that connect these L-values with Mahler measures for several families of polynomials.

Feb 13

A new proof of the arithmetic Siegel-Weil formula

Joey Yu Luo (UW-Madison)

The arithmetic Siegel-Weil formula establishes a profound connection between intersection numbers in Shimura varieties and the Fourier coefficients of central derivatives of Eisenstein series. This result was proven by C. Li and W. Zhang in 2021 using local methods. In this talk, I will present a new proof of the formula that uses the local-global compatibility and the modularity of generating series of special divisors.