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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/
Contact:
Barb Hodgson | hodgsonb@uleth.ca | (403) 329-2470 | uleth.ca/artsci/math-computer-science