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Edward Herman","submitted_at":"2013-05-06T16:54:15Z","abstract_excerpt":"We give more evidence for Patterson's conjecture on sums of exponential sums, by getting an asymptotic for a sum of quartic exponential sums over $\\Q[i].$ Previously, the strongest evidence of Patterson's conjecture over a number field is the paper of Livn\\'{e} and Patterson \\cite{LP} on sums of cubic exponential sums over $\\Q[\\omega], \\omega^3=1.$\n  The key ideas in getting such an asymptotic are a Kuznetsov-like trace formula for metaplectic forms over a quartic cover of $GL_2,$ and an identity on exponential sums relating Kloosterman sums and quartic exponential sums. 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