Advertisement

Intersections of Two Walls of the Gottschling Fundamental Domain of the Siegel Modular Group of Genus Two

  • Takayuki OdaEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 115)

Abstract

If one has a chance to see the classical books of Fricke-Klein on modular functions of one variable, which were written one hundred years ago, one can find many beautiful pictures of fundamental domains bounded by geodesic lines with respect to the invariant hyperbolic metric in the complex upper half plane \(\mathfrak{H}_{1}\).

Keywords

Fundamental Domain Siegel Modular Group Modular Elliptic Curves Modular Symbols Harmonic Differential Forms 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Gottschling, Erhard, Explizite Bestimmung der Randflächen des Fundamentalbereiches des der Modulgruppe zweiten Grades. Math. Ann. 138, 103–124 (1959)Google Scholar
  2. 2.
    T. Hayata, T. Oda, T. Yatouda, Zero cells of the Siegel-Gottschling fundamental domain of genus 2. Experimental Math. 21(3), 266–279 (2012)CrossRefzbMATHGoogle Scholar
  3. 3.
    J.-P. Labesse, J. Schwermer (eds), Cohomology of Arithmetic Groups and Automorphic Forms, Proceedings of Conference held in Luminy/Marseille, May 1989, Lecure Notes im Math. vol. 1447 (Springer, NewYork)Google Scholar
  4. 4.
    T. Oda, in Geometry and Analysis of Automorphic Forms of Several Variables, Cohomology Of Siegel Modular Varieties Of Genus 2 and Corresponding Automorphic Forms (World Scientific, Singapore, 2011) pp. 211–253Google Scholar
  5. 5.
    S. Takashi, Riemannian Geometry, Translations of Mathematical Monographs, vol. 149 (American Mathematical Society, Providence 1992)Google Scholar
  6. 6.
    C.L. Siegel, Symplectic geometry. Amer. J. Math. 65, 1–86 (1943); the book of Academic Press with the same title (1964)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.The University of TokyoTokyoJapan

Personalised recommendations