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Class fields over real quadratic fields in the theory of modular functions

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Several Complex Variables II Maryland 1970

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 185))

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References

  1. W. Casselman, Some new abelian varieties with good reduction, to appear.

    Google Scholar 

  2. P. Deligne, Formes modulaires et représentations l-adiques, Séminaire Bourbaki, février 1969, exposé 355.

    Google Scholar 

  3. E. Hecke, Zur Theorie der elliptischen Funktionen, Math. Ann. 97 (1926), 210–242 (=Werke, 428–460).

    Article  MathSciNet  MATH  Google Scholar 

  4. —, Analytische Arithmetik der positiven quadratischen Formen, Danske Vid. Selsk. Mat.-Fys. Medd. XVII, 12 (Kobenhavn 1940) (=Werke, 789–918).

    Google Scholar 

  5. H. Maass, Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann. 121 (1949), 141–183.

    Article  MathSciNet  MATH  Google Scholar 

  6. T. Miyake, Decomposition of Jacobian varieties and Dirichlet series of Hecke type, to appear.

    Google Scholar 

  7. G. Shimura, Class-fields and automorphic functions, Ann. of Math. (2) 80 (1964), 444–463.

    Article  MathSciNet  MATH  Google Scholar 

  8. —, Construction of class fields and zeta functions of algebraic curves, Ann. of Math. (2) 85 (1967), 58–159.

    Article  MathSciNet  MATH  Google Scholar 

  9. —, On canonical models of arithmetic quotients of bounded symmetric domains, Ann. of Math. (2) 91 (1970), 140–222.

    MathSciNet  MATH  Google Scholar 

  10. —, Introduction to the arithmetic theory of automorphic functions, to appear.

    Google Scholar 

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John Horváth

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© 1971 Springer-Verlag

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Shimura, G. (1971). Class fields over real quadratic fields in the theory of modular functions. In: Horváth, J. (eds) Several Complex Variables II Maryland 1970. Lecture Notes in Mathematics, vol 185. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058770

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  • DOI: https://doi.org/10.1007/BFb0058770

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05372-9

  • Online ISBN: 978-3-540-36493-1

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