Fourier Interpolation and the Weil Representation
Heilbronn Number Theory Seminar
27th September 2023, 4:00 pm – 5:00 pm
Fry Building, 2.04
In 2017, Radchenko-Viazovska proved a remarkable interpolation result for even Schwartz functions on the real line: such a function is entirely determined by its values and those of its Fourier transform at square roots of integers. We give a new proof of this result, exploiting the fact that Schwartz functions are the underlying vector space of the Weil representation W. This allows us to deduce the interpolation result from the computation of the cohomology of a certain congruence subgroup of SL2(Z) with values in W by relating it to spaces of modular forms. This is joint work in progress with Akshay Venkatesh.
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