A generalization of Eichler's trace formula

• Autores: Juliusz Brzezinski
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 48, Fasc. 1-2, 1997, págs. 53-62
• Idioma: inglés
• Enlaces
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• Resumen

  • Eichler’s trace formula for traces of the Brandt-Eichler matrices is proved for arbitrary totally definite orders in central simple algebras of prime index over global fields. A formula for type numbers of such orders is proved as an application.

• Referencias bibliográficas
  • J. Brzezinski, A Combinatorial Class Number Formula, J. Reine Angew. Math. 402 (1989), 199–210.
  • J. Brzezinski, On Automorphisms of Quaternion Orders, J. Reine Angew. Math. 403 (1990), 166–186.
  • C.W. Curtis and I. Reiner, Methods of Representation Theory, vol. I, Academic Press, New York, 1981.
  • M. Denert and J. Van Geel, The Class Number of Hereditary Orders in non-Eichler Algebras over Global Function Fields, Math. Ann. 282 (1988),...
  • M. Eichler, Zur Zahlentheorie der Quaternionenalgebren, J. Reine Angew. Math. 195 (1955), 127–151.
  • H. Hijikata, A. Pizer and T. Shemanske, Orders in Quaternion Algebras, J. Reine Angew. Math. 394 (1989), 59–106.
  • O. Körner, Traces of Eichler-Brandt matrices and type numbers of quaternion orders, Proc. Indian Acad. Sci. Math. Sci. 97 (1987), 189–199.
  • M. Peters, Ternäre und quaternäre quadratische Formen und Quaternionen Algebren, Acta Arith. 15 (1969), 329–365.
  • A. Pizer, Type Numbers of Eichler Orders, J. Reine Angew. Math. 264 (1973), 76–102.
  • A. Pizer, Theta series and modular forms of level $p^2M$, Compositio Math. 40 (1980), 177–241.
  • M.-F. Vignéras, Arithmétique des Algèbres de Quaternions, Lect. Notes in Math. 800, Springer-Verlag, Berlin-Heidelberg-New York, 1980.