Jack Buttcane‘s current research is on the use of techniques from classical analytic number theory in the study of higher-rank automorphic forms. He hopes to apply these methods to classical equidistribution problems and problems related to polynomials and primes. His interests and methods are in analytic number theory, harmonic analysis on symmetric spaces, complex analysis, the spectral theory of automorphic forms, trace formulas, exponential sums, and L-functions.
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