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Department of Mathematics,
Department of Mathematics,
University of California San Diego
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Undergraduate Honors Presentation
Michael Hoffman
University of California, San Diego
Conjecture of Gross - Fourier Coefficients on $G_2$ and Cubic Twist L-Values Part II
Abstract:
Benedict Gross has a conjecture relating the square roots of the central values of a certain L-function of a cuspidal eigenform $f$ to the Fourier coefficients of the lift of $f$ to the group $G_2$. We describe methods to compute the central values of the L-function of $f$, twisted by a Dirichlet character associated to a Galois cubic field. We will provide evidence for this conjecture of Gross via comparison with Fourier coefficients on $G_2$ computed by Aaron Pollack. This is joint work with Maya Chang.
Advisor: Professor Aaron Pollack
May 6, 2026
2:00 PM
APM 7321
Research Areas
Number Theory****************************
