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Volumn 80, Issue 1, 1997, Pages 1-48

A stationary phase formula for exponential sums over ℤ/pmℤ and applications to GL(3)-Kloosterman sums

Author keywords

Exponential sums; Fourier coefficients of automorphic forms

Indexed keywords


EID: 0031456283     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa-80-1-1-48     Document Type: Article
Times cited : (50)

References (29)
  • 2
    • 0002391725 scopus 로고
    • Poincaré series and Kloosterman sums for SL(3, ℤ)
    • D. Bump, S. Friedberg and D. Goldfeld, Poincaré series and Kloosterman sums for SL(3, ℤ), Acta Arith. 50 (1988), 31-89.
    • (1988) Acta Arith. , vol.50 , pp. 31-89
    • Bump, D.1    Friedberg, S.2    Goldfeld, D.3
  • 5
    • 0000845279 scopus 로고
    • Applications de la formule des traces aux sommes trigonomé-triques
    • Springer, Berlin
    • P. Deligne, Applications de la formule des traces aux sommes trigonomé-triques, in: SGA 4 1/2, Lecture Notes in Math. 569, Springer, Berlin, 1977.
    • (1977) SGA 4 1/2, Lecture Notes in Math. , vol.569
    • Deligne, P.1
  • 7
    • 0010668699 scopus 로고    scopus 로고
    • A note on Hensel's lemma in several variables
    • to appear
    • B. Fisher, A note on Hensel's lemma in several variables, Proc. Amer. Math. Soc., to appear.
    • Proc. Amer. Math. Soc.
    • Fisher, B.1
  • 8
    • 0000219223 scopus 로고
    • Poincaré series for GL(n): Fourier expansion, Kloosterman sums and algebreo-geometric estimates
    • S. Friedberg, Poincaré series for GL(n): Fourier expansion, Kloosterman sums and algebreo-geometric estimates, Math. Z. 196 (1987), 165-188.
    • (1987) Math. Z. , vol.196 , pp. 165-188
    • Friedberg, S.1
  • 9
    • 51249187593 scopus 로고
    • Rational points in Henselian discrete valuation rings
    • M. Greenberg, Rational points in Henselian discrete valuation rings, Publ. Math. IHES 31 (1966), 59-64.
    • (1966) Publ. Math. IHES , vol.31 , pp. 59-64
    • Greenberg, M.1
  • 11
    • 0010706837 scopus 로고
    • Séminaire de géométrie algébrique du bois-marie
    • Springer, Berlin
    • _, Séminaire de Géométrie Algébrique du Bois-Marie, SGA 1 Chapter II, Lecture Notes in Math. 224, Springer, Berlin, 1971.
    • (1971) SGA 1 Chapter II, Lecture Notes in Math. , vol.224
  • 13
    • 0000374886 scopus 로고
    • Travaux de laumon
    • N. Katz, Travaux de Laumon, Astérisque 161-162 (1988), 105-132.
    • (1988) Astérisque , vol.161-162 , pp. 105-132
    • Katz, N.1
  • 14
    • 0003224140 scopus 로고
    • Gauss sums, Kloosterman sums and monodromy groups
    • Princeton Univ. Press, Princeton
    • _, Gauss Sums, Kloosterman Sums and Monodromy Groups, Ann. of Math. Stud. 116, Princeton Univ. Press, Princeton, 1988.
    • (1988) Ann. of Math. Stud. , vol.116
  • 15
    • 0003323999 scopus 로고
    • Exponential sums and differential equations
    • Princeton Univ. Press, Princeton
    • _, Exponential Sums and Differential Equations, Ann. of Math. Stud. 124, Princeton Univ. Press, Princeton, 1990.
    • (1990) Ann. of Math. Stud. , vol.124
  • 17
    • 0010750373 scopus 로고    scopus 로고
    • Appendix in [B-F-G]
    • M. Larsen, Appendix in [B-F-G].
    • Larsen, M.1
  • 19
    • 84959785314 scopus 로고
    • On Hua's estimate for exponential sums
    • _, _, On Hua's estimate for exponential sums, J. London Math. Soc. 26 (1982), 15-20.
    • (1982) J. London Math. Soc. , vol.26 , pp. 15-20
  • 20
    • 0001610349 scopus 로고
    • The estimation of complete exponential sums
    • J. H. Loxton and R. C. Vaughan, The estimation of complete exponential sums, Canad. Math. Bull. 28 (1985), 440-454.
    • (1985) Canad. Math. Bull. , vol.28 , pp. 440-454
    • Loxton, J.H.1    Vaughan, R.C.2
  • 22
    • 0003263492 scopus 로고
    • The red book of varieties and schemes
    • Springer, Berlin
    • D. Mumford, The Red Book of Varieties and Schemes, Lecture Notes in Math. 1358, Springer, Berlin, 1988.
    • (1988) Lecture Notes in Math. , vol.1358
    • Mumford, D.1
  • 23
    • 0001770692 scopus 로고
    • Über die Kloostermanschen Summen S(u, v; q)
    • H. Salié, Über die Kloostermanschen Summen S(u, v; q), Math. Z. 34 (1931), 91-109.
    • (1931) Math. Z. , vol.34 , pp. 91-109
    • Salié, H.1
  • 24
    • 0002739011 scopus 로고
    • On the estimation of Fourier coefficients of modular forms
    • Amer. Math. Soc.
    • A. Selberg, On the estimation of Fourier coefficients of modular forms, in: Proc. Sympos. Pure Math. 8, Amer. Math. Soc., 1965, 1-15.
    • (1965) Proc. Sympos. Pure Math. , vol.8 , pp. 1-15
    • Selberg, A.1
  • 25
    • 0001313736 scopus 로고
    • On n-dimensional Kloosterman sums
    • R. A. Smith, On n-dimensional Kloosterman sums, J. Number Theory 11 (1979), 324-343.
    • (1979) J. Number Theory , vol.11 , pp. 324-343
    • Smith, R.A.1
  • 26
    • 84966253823 scopus 로고
    • Estimates for exponential sums
    • _, Estimates for exponential sums, Proc. Amer. Math. Soc. 79 (1980), 365-368.
    • (1980) Proc. Amer. Math. Soc. , vol.79 , pp. 365-368
  • 27
    • 34250103369 scopus 로고
    • Poincaré series on GL(r) and Kloosterman sums
    • G. Stevens, Poincaré series on GL(r) and Kloosterman sums, Math. Ann. 277 (1987), 25-51.
    • (1987) Math. Ann. , vol.277 , pp. 25-51
    • Stevens, G.1
  • 28
    • 0001303344 scopus 로고
    • On some exponential sums
    • A. Weil, On some exponential sums, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 204-207.
    • (1948) Proc. Nat. Acad. Sci. U.S.A. , vol.34 , pp. 204-207
    • Weil, A.1
  • 29
    • 34250594733 scopus 로고
    • Sur certains groupes d'opérateurs unitaires
    • _, Sur certains groupes d'opérateurs unitaires, Acta Math. 111 (1964), 143-211.
    • (1964) Acta Math. , vol.111 , pp. 143-211


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