1. A conjecture of Evans on sums of Kloosterman sums.
- Author
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Evan P. Dummit, Adam W. Goldberg, and Alexander R. Perry
- Subjects
- *
LOGICAL prediction , *KLOOSTERMAN sums , *SHEAF theory , *HYPERGEOMETRIC functions , *MODULAR forms , *GEOMETRIC congruences - 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 $T_n$ 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 $T_n$ with generalized Apéry numbers. [ABSTRACT FROM AUTHOR]
- Published
- 2010
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