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Gauss sums and elliptic functions: II. The quartic sum

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References

  • [C] Cassels, J.W.S.: On Kummer sums. Proc. London Math. Soc.21, 19–27 (1970)

    Google Scholar 

  • [DH] Davenport, H., Hasse, H.: Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen. J. reine angew. Math.172, 151–182 (1934)

    Google Scholar 

  • [E] Eisenstein, G.: Mathematische Werke Bd. II. New York: Chelsea 1975

    Google Scholar 

  • [G] Gunji, H.: The Hasse invariat andp-division points of an elliptic curve. Arch. Math.27, 148–157 (1976)

    Google Scholar 

  • [H1] Hasse, H.: Vorlesungen über Zahlentheorie. Berlin: Springer 1950

    Google Scholar 

  • [H2] Hasse, H.: Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper, Bd. II. Leipzig/Berlin 1930

  • [H3] Hecke, E.: Mathematische Werke. Gottingen: Vanderhoeck and Ruprecht 1959

    Google Scholar 

  • [K1] Kubota, T.: Reciprocities in Gauss' and Eisenstein's number fields. J. reine angew. Math.208, 35–50 (1961)

    Google Scholar 

  • [K2] Kubota, T.: Some arithmetical applications of an elliptic function. J. reine angew. Math.214/5, 141–145 (1964)

    Google Scholar 

  • [K3] Kubota, T.: An application of the power residue theory to some abelian functions. Nagoya Math. J.27, 51–54 (1966)

    Google Scholar 

  • [L] Loxton, J.H.: Some conjectures concerning Gauss sums. J. reine angew. Math.297, 153–158 (1978)

    Google Scholar 

  • [M1] McGettrick, A.D.: On Gaussian sums. Dissertation, Cambridge 1970

  • [M2] McGettrick, A.D.: On the biquadratic Gauss sum. Proc. Cambridge Phil. Soc.71, 79–83 (1972)

    Google Scholar 

  • [M3] Matthews, C.R.: Gauss sums and elliptic functions. Dissertation, Cambridge 1978

  • [M4] Matthews, C.R.: Gauss sums and elliptic functions: I. The Kummer sum. Invent. math.52, 163–185 (1979)

    Google Scholar 

  • [R1] Rademacher, H., Grosswald, E.: Dedekind sums. Carus monograph No 16, Math. Assoc. of America 1972

  • [R2] Robert, A.: Elliptic Curves. Lecture Notes in Mathematics 326. Berlin, Heidelberg, New York: Springer-Verlag 1973

    Google Scholar 

  • [S] Serre, J.-P.: Local class field theory. Algebraic Number Theory (J.W.S. Cassels and A. Frohlich eds.). New York, London: Academic Press 1967

    Google Scholar 

  • [W1] Weil, A.: La cyclotomie jadis et naguère. Séminaire Bourbaki 452 (1973–74)

  • [W2] Whittaker, E.T., Watson, G.N.: A course of modern analysis (4th edition). Cambridge, at the University Press 1962

    Google Scholar 

  • [Y] Yamamoto, K.: On Gaussian sums with biquadratic residue characters. J. reine angew. Math.219, 200–213 (1965)

    Google Scholar 

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Matthews, C.R. Gauss sums and elliptic functions: II. The quartic sum. Invent Math 54, 23–52 (1979). https://doi.org/10.1007/BF01391175

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