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Lethbridge Number Theory and Combinatorics Seminar
Monday, March 25
12-12:50 p.m.
D631 University Hall
Qing Zhang (University of Calgary)
On the holomophy of adjoint L-function for GL(3)
L-functions associated with automorphic forms are vast generalizations of Riemann zeta functions and Dirichlet L-functions. Although the theory of L-functions play a fundamental role in number theory, it is still largely conjectural. If pi is an irreducible cuspidal automorphic representation of GL_n over a number field F and pi* is its dual representation, it is conjectured that the Dedekind zeta function zeta_F(s) (which is the Riemann zeta function when F is the field Q of rational numbers) "divides" the Rankin-Selberg L-function L(s, pi x \pi*), i.e., the quotient (which is called the adjoint L-function of pi) should be entire. For n = 2, this conjecture was proved by Gelbart-Jacquet.
In this talk, I will give a sketchy survey of constructions of some L-functions, including the Rankin-Selberg L-function L(s, pi_1 x \pi_2), and report our recent work on the above conjecture when n = 3. This is a joint work with Joseph Hundley.
Contact:
Barb Hodgson | hodgsonb@uleth.ca | (403) 329-2470