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Sol Friedberg : Higher theta functions

Higher theta functions are the residues of Eisenstein series on covers of the adelic points of classical groups. On the one hand, they generalize the Jacobi theta function. On the other, their Whittaker-Fourier coefficients are not understood, even for covers of $GL_2$. In this talk I explain how, using methods of descent, one may establish a series of relations between the coefficients of theta functions on different groups. In the first instance, this allows us to prove a version of Patterson's famous conjecture relating the Fourier coefficient of the biquadratic theta function to quartic Gauss sums. This is based on joint work with David Ginzburg.

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