Geodesic
On twisted Kloosterman sums
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 19, Tome 302 (2003), pp. 96-106

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For the Kloosterman sums twisted by characters over a finite field, addition formulas of convolution type are derived. As a corollary, orthogonality relations connecting the Kloosterman and Salié vectors are obtained. 
@article{ZNSL_2003_302_a6,
     author = {N. V. Proskurin},
     title = {On twisted {Kloosterman} sums},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {96--106},
     publisher = {mathdoc},
     volume = {302},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_302_a6/}
}
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N. V. Proskurin. On twisted Kloosterman sums. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 19, Tome 302 (2003), pp. 96-106. http://geodesic.mathdoc.fr/item/ZNSL_2003_302_a6/