On multiple Salié sums
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- by W. Duke
- Proc. Amer. Math. Soc. 114 (1992), 623-625
- DOI: https://doi.org/10.1090/S0002-9939-1992-1077785-2
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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 H. Davenport and H. Hasse, Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen, J. Reine Angew. Math. 172 (1934), 151-182.
- 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
Bibliographic Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 623-625
- MSC: Primary 11L05; Secondary 11F55, 11T23
- DOI: https://doi.org/10.1090/S0002-9939-1992-1077785-2
- MathSciNet review: 1077785