Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A conjecture of Evans on sums of Kloosterman sums

Author(s): Evan P. Dummit; Adam W. Goldberg; Alexander R. Perry
Journal: Proc. Amer. Math. Soc. 138 (2010), 3047-3056.
MSC (2010): Primary 11L05; Secondary 33C20
Posted: May 4, 2010
MathSciNet review: 2653929
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Abstract: In a recent paper, Evans relates twisted Kloosterman sheaf sums to Gaussian hypergeometric functions, and he formulates a number of conjectures relating certain twisted Kloosterman sheaf sums to the coefficients of modular forms. Here we prove one of his conjectures for a fourth order twisted Kloosterman sheaf sum of the quadratic character on $\mathbf{F}_p^\times$ . In the course of the proof we develop reductions for twisted moments of Kloosterman sums and apply these in the end to derive a congruence relation for with generalized Apéry numbers.

References:

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