Automorphic L-Functions, Fourier Coefficients, and Applications

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The project involves investigations in the analytic theory of automorphic forms. The PI will work with Wilfried Schmid on creating L-functions from automorphic boundary value distributions, and seeks to generalize their archimedean methods to p-adic fields. The PI will also work with the string theorists Michael Green and Pierre Vanhove on automorphic realizations of small real group representations and their Fourier coefficients. Their goal is to produce examples on exceptional groups which shed light on graviton scattering amplitudes. Finally, the PI will work with the cryptographer Ramarathnam Venkatesan on lattice approaches to cryptographic problems.Automorphic forms are a central topic in modern number theory, and their L-functions relate them to an even wider range of current investigations. The work with Green and Vanhove has used automorphic forms to solve questions commonly studied in the string theory literature. The project with Venkatesan studies the security of commonly used commercial cryptographic algorithms.