Geodesic
On Salié's sum
Glasgow mathematical journal, Tome 14 (1973) no. 1, pp. 25-26

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Let p be an odd prime and let f(x) be a complex-valued function such that f(x+p) = f(x) for all integers x. Write e(x) = exp(2πix/p), and define l/x by , where We consider the sumwhere is the Legendre symbol. The sum is zero if as is clear on replacing x by bjax. Salié has found a result which can be written in the formwhen h2 ≡ 4ab(modp). 
Mordell, L. J. On Salié's sum. Glasgow mathematical journal, Tome 14 (1973) no. 1, pp. 25-26. doi: 10.1017/S0017089500001695
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[1] 1.Mordell, L. J., On some exponential sums related to Kloosterman sums, Ada Arithmetical to appear. Google Scholar

[2] 2.Williams, K. S., On Salié's sum, J. Number Theory 3 (1971), 316–317. Google Scholar | DOI

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