# Moments of Kloosterman sums and modular forms

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Kloosterman sum is one of the most famous exponential sums

in number theory. It is defined using a prime p (and another number).

How do these sums vary with p? Ron Evans has made several conjectures

relating the moment of Kloosterman sums for p to the p-th Fourier

coefficient of certain modular forms. We sketch a proof of his

conjectures.