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Soluzioni algebriche dell’equazione di Lamé e torsione delle curve ellittiche

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Si discute il legame esistente tra equazioni di LaméL n conn intero e soluzioni tutte algebriche, e punti di torsione di curve ellittiche. In particolare si esibisce una equazioneL 1 con gruppo di monodromia proiettivo su

diedrale di ordine 6, legata ai punti di 3-divisione della curvay 2=4x 3−1.

Summary

We discuss the relation between Lamé equationsL n with integraln and only algebraic solutions, and torsion points of elliptic curves. In particular we exhibit an equationL 1 with projective monodromy group over

dihedral of order 6, related to the 3-division points of the curvey 2=4x 3−1.

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Bibliografia

  1. Baldassarri F. andDwork B.,On second order linear differential equations with algebraic solutions. Amer. J. Math. 101 (1979), 42–76.

    Article  MATH  MathSciNet  Google Scholar 

  2. Baldassarri F.,On second order linear differential equations with algebraic solutions on algebraic curves. Amer. J. Math. 102 (1980), 517–535.

    Article  MATH  MathSciNet  Google Scholar 

  3. Baldassarri F.,On algebraic solutions of Lamé’s differential equation. J. Diff. Eq. 41 (1981), 44–58.

    Article  MATH  MathSciNet  Google Scholar 

  4. Chudnovsky D. V. and G. V.,Applications of Padé approximations to the Grothendieck conjecture on linear differential equations. In «Number Theory», New York 1984, Lecture Notes in Math. 1135, 52–100.

  5. Dwork B.,Arthmetic theory of differential equations. Symp. Math. XXIV (1981), 225–243.

    MathSciNet  Google Scholar 

  6. Katz N.,Algebraic solutions of differential equations. Invent. Math. 18 (1972), 1–118.

    Article  MATH  MathSciNet  Google Scholar 

  7. Poole E. G. C.,Introduction to the theory of linear differential equations. Oxford University Press, Oxford 1936.

    Google Scholar 

  8. Whittaker E. T. andWatson G. N.,A course of modern analysis. Cambridge University Press, 4-th edition, Cambridge 1927.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Università di Padova, Padova, Italia

    F. Baldassarri

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  1. F. Baldassarri
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Baldassarri, F. Soluzioni algebriche dell’equazione di Lamé e torsione delle curve ellittiche. Seminario Mat. e. Fis. di Milano 57, 203–213 (1987). https://doi.org/10.1007/BF02925051

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  • DOI: https://doi.org/10.1007/BF02925051

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