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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The lifting of an exponential sum
to a cyclic algebraic number field
of prime degree


Author: Yangbo Ye
Journal: Trans. Amer. Math. Soc. 350 (1998), 5003-5015
MSC (1991): Primary 11L05; Secondary 11F70
DOI: https://doi.org/10.1090/S0002-9947-98-02001-7
MathSciNet review: 1433129
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $E$ be a cyclic algebraic number field of prime degree. We prove an identity which lifts an exponential sum similar to the Kloosterman sum to an exponential sum taken over certain algebraic integers in $E$.


References [Enhancements On Off] (What's this?)

  • 1. H. Cohen, A Course in Computational Algebraic Number Theory, Springer: Berlin-Heidelberg-New York 1993. MR 94i:11105
  • 2. H. Davenport and H. Hasse, Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen, J. Reine Angew. Math. 172 (1935), 151-182.
  • 3. W. Duke and H. Iwaniec, A relation between cubic exponential and Kloosterman sums, Contemporary Math. 143 (1993), 255-258. MR 93m:11082
  • 4. J. Greene and D. Stanton, The triplication formula for Gauss sums, Aequationes Math. 30 (1986), 134-141. MR 87g:11162
  • 5. P. Gérardin and J.P. Labesse, The solution of a base change problem for $GL(2)$ (following Langlands, Saito, Shintani), Proc. Symp. Pure Math. 33 (1979), part 2, 115-133. MR 82e:10047
  • 6. H. Jacquet, The continuous spectrum of the relative trace formula for $GL(3)$ over a quadratic extension, Israel J. Math. 89 (1995), 1-59. MR 96a:22029
  • 7. H. Jacquet and R.P. Langlands, Automorphic Forms on $GL(2)$, Lecture Notes in Math. Vol. 114, Springer: Berlin-Heidelberg-New York, 1970. MR 53:5481
  • 8. H. Jacquet and Y. Ye, Une remarque sur le changement de base quadratique, C. R. Acad. Sci. Paris Ser. I Math. 311 (1990), 671-676. MR 92j:11046
  • 9. N.M. Katz, Gauss Sums, Kloosterman Sums, and Monodromy Groups, Ann. Math. Studies, No. 116, Princeton Univ. Press: Princeton 1988. MR 91a:11028
  • 10. D.S. Kubert and S. Lichtenbaum, Jacobi-sum Hecke characters and Gauss-sum identities, Comp. Math. 48 (1983), 55-87. MR 85c:11108
  • 11. Z. Mao and S. Rallis, A trace formula for dual pairs, Duke Math. J. 87 (1997), 321-341. CMP 97:11
  • 12. J. Tate, Number theoretic background, Proc. Symp. Pure Math. 33 (1979), part 2, 3-26. MR 80m:12009
  • 13. Y. Ye, Kloosterman integrals and base change for $GL(2)$, J. Reine Angew. Math. 400 (1989), 57-121. MR 90i:11134
  • 14. Y. Ye, The lifting of Kloosterman sums, J. Number Theory, 51 (1995), 275-287. MR 97a:11126
  • 15. D. Zagier, Modular forms associated to real quadratic fields, Invent. Math. 30 (1975), 1-46. MR 52:3062

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Additional Information

Yangbo Ye
Affiliation: Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242-1419
Email: yey@math.uiowa.edu

DOI: https://doi.org/10.1090/S0002-9947-98-02001-7
Received by editor(s): May 13, 1996
Received by editor(s) in revised form: December 9, 1996
Article copyright: © Copyright 1998 American Mathematical Society

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