Notice Board

Lethbridge Number Theory and Combinatorics Seminar

Date:

August 27, 2018

Time:

11:00 - 11:50 a.m.

Lecturer(s):

Allysa Lumley (York University)

Location:

University of Lethbridge

Topic:

Distribution of Values of L-functions associated to Hyperelliptic Curves over Finite Fields

Description:

In 1992, Hoffstein and Rosen proved a function field analogue to Gauss' conjecture (proven by

Siegel) regarding the class number h_D, of a discriminant D by averaging over all polynomials with a fixed degree. In this case h_D = |Pic(O_D)|, where Pic(O_D) is the Picard group of O_D.

Andrade later considered the average value of h_D, where D is monic, squarefree and its degree

2g+1 varies. He achieved these results by calculating the first moment

2g+of L(1,chi_D) in combination

with Artin's formula relating L(1,chi_D) and h_D. Later, Jung averaged L(1, chi_D) over monic, squarefree polynomials with degree 2g+2 varying. Making use of the second case of Artin's formula he gives results about h_D R_D, where R_D is the regulator of O_D.

For this talk we discuss the complex moments of L(1,chi_D), with D monic, squarefree and degree n varying. Using this information we can describe the distribution of values of L(1,chi_D) and after specializing to n=2g+1 we give results about h_D and specializing to n=2g+2 we give results about h_D R_D.

Other Information:

Location: C630 University Hall

Web page: http://www.cs.uleth.ca/~nathanng/ntcoseminar/