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Number Theory Seminar

Thursday, October 13, 2022
4:00pm to 5:00pm
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Linde Hall 387
Modular forms of half-integral weight on G_2
Aaron Pollack, Department of Mathematics, UCSD,

Classical holomorphic modular forms are number-theoretic objects that have been intensely studied. The split exceptional group G_2 does not support a theory of holomorphic modular forms, but it does possess so-called quaternionic modular forms. These are a special class of automorphic forms that appear to behave similarly to holomorphic modular forms. In the talk, I will describe a theory of modular forms of half-integral weight on G_2 and other exceptional groups. In particular, we prove the existence of a modular form of weight 1/2 on G_2 whose Fourier coefficients are related to the 2-torsion in the narrow class groups of totally real cubic fields. This is joint work with Spencer Leslie.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].