On multiple Salié sums

Duke, W.

doi:10.1090/S0002-9939-1992-1077785-2

On multiple Salié sums
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by W. Duke PDF

Proc. Amer. Math. Soc. 114 (1992), 623-625 Request permission

Abstract:

This note shows that the Davenport-Hasse relation for Gauss sums is equivalent to the evaluation of some multidimensional exponential sums that generalize that of Salié.

References

Daniel Bump, Solomon Friedberg, and Dorian Goldfeld, Poincaré series and Kloosterman sums for $\textrm {SL}(3,\textbf {Z})$, Acta Arith. 50 (1988), no. 1, 31–89. MR 945275, DOI 10.4064/aa-50-1-31-89
Daniel Bump and Jeffrey Hoffstein, Cubic metaplectic forms on $\textrm {GL}(3)$, Invent. Math. 84 (1986), no. 3, 481–505. MR 837524, DOI 10.1007/BF01388743

Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen

172

John Greene and Dennis Stanton, The triplication formula for Gauss sums, Aequationes Math. 30 (1986), no. 2-3, 134–141. MR 843655, DOI 10.1007/BF02189920
Henryk Iwaniec, Fourier coefficients of modular forms of half-integral weight, Invent. Math. 87 (1987), no. 2, 385–401. MR 870736, DOI 10.1007/BF01389423
Serge Lang, Cyclotomic fields, Graduate Texts in Mathematics, Vol. 59, Springer-Verlag, New York-Heidelberg, 1978. MR 0485768, DOI 10.1007/978-1-4612-9945-5
Rudolf Lidl and Harald Niederreiter, Finite fields, Encyclopedia of Mathematics and its Applications, vol. 20, Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1983. With a foreword by P. M. Cohn. MR 746963
L. J. Mordell, On some exponential sums related to Kloosterman sums, Acta Arith. 21 (1972), 65–69. MR 306133, DOI 10.4064/aa-21-1-65-69
Hans Salié, Über die Kloostermanschen Summen $S(u,v;q)$, Math. Z. 34 (1932), no. 1, 91–109 (German). MR 1545243, DOI 10.1007/BF01180579
Kenneth S. Williams, Note on Salié’s sum, Proc. Amer. Math. Soc. 30 (1971), 393–394. MR 284408, DOI 10.1090/S0002-9939-1971-0284408-5