Quadratic modular symbols on Shimura curves

Pilar Bayer[1]; Iván Blanco-Chacón[2]

  • [1] Facultat de Matemàtiques Universitat de Barcelona Gran Via de les Corts Catalanes, 585 08007 Barcelona, Spain
  • [2] Department of Mathematics and Systems Analysis Aalto University Otakaari 1, M FI-00076 Espoo, Finland

Journal de Théorie des Nombres de Bordeaux (2013)

  • Volume: 25, Issue: 2, page 261-283
  • ISSN: 1246-7405

Abstract

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We introduce the concept of quadratic modular symbol and study how these symbols are related to quadratic p -adic L -functions. These objects were introduced in [3] in the case of modular curves. In this paper, we discuss a method to attach quadratic modular symbols and quadratic p -adic L -functions to more general Shimura curves.

How to cite

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Bayer, Pilar, and Blanco-Chacón, Iván. "Quadratic modular symbols on Shimura curves." Journal de Théorie des Nombres de Bordeaux 25.2 (2013): 261-283. <http://eudml.org/doc/275719>.

@article{Bayer2013,
abstract = {We introduce the concept of quadratic modular symbol and study how these symbols are related to quadratic$p$-adic $L$-functions. These objects were introduced in [3] in the case of modular curves. In this paper, we discuss a method to attach quadratic modular symbols and quadratic $p$-adic $L$-functions to more general Shimura curves.},
affiliation = {Facultat de Matemàtiques Universitat de Barcelona Gran Via de les Corts Catalanes, 585 08007 Barcelona, Spain; Department of Mathematics and Systems Analysis Aalto University Otakaari 1, M FI-00076 Espoo, Finland},
author = {Bayer, Pilar, Blanco-Chacón, Iván},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Shimura curve; modular symbol; -function},
language = {eng},
month = {9},
number = {2},
pages = {261-283},
publisher = {Société Arithmétique de Bordeaux},
title = {Quadratic modular symbols on Shimura curves},
url = {http://eudml.org/doc/275719},
volume = {25},
year = {2013},
}

TY - JOUR
AU - Bayer, Pilar
AU - Blanco-Chacón, Iván
TI - Quadratic modular symbols on Shimura curves
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2013/9//
PB - Société Arithmétique de Bordeaux
VL - 25
IS - 2
SP - 261
EP - 283
AB - We introduce the concept of quadratic modular symbol and study how these symbols are related to quadratic$p$-adic $L$-functions. These objects were introduced in [3] in the case of modular curves. In this paper, we discuss a method to attach quadratic modular symbols and quadratic $p$-adic $L$-functions to more general Shimura curves.
LA - eng
KW - Shimura curve; modular symbol; -function
UR - http://eudml.org/doc/275719
ER -

References

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  11. R. Pollack, G. Stevens, Overconvergent modular symbols and p -adic L -functions. Ann. Sci. Éc. Norm. Sup. 44, n. 1 (2011), 1–42. Zbl1268.11075MR2760194
  12. A. M. Robert, A course in p -adic analysis. Graduate Texts in Mathematics 198, Springer, 2000. Zbl0947.11035MR1760253
  13. D. E. Rohrlich, L -functions and division towers. Math. Ann. 281 (1988), 611–632. Zbl0656.14013MR958262
  14. G. Shimura, Construction of class fields and zeta functions of algebraic curves. Ann. of Math. 85, n. 2 (1967), 58–159. Zbl0204.07201MR204426
  15. G. Shimura, Introduction to the arithmetic theory of automorphic forms. Princeton University Press, 1971. Zbl0221.10029
  16. K. Takeuchi, Arithmetic Fuchsian groups with signature ( 1 ; e ) . J. Math. Soc. Japan 35, n. 3 (1983), 381–407. Zbl0517.20022MR702765
  17. M. F. Vignéras, Arithmétique des algèbres de quaternions. Lecture Notes in Mathematics 800. Springer, 1980. Zbl0422.12008MR580949
  18. Y. Yang, Schwarzian differential equations and Hecke eigenforms on Shimura curves. arXiv: 1110.6284v1, 2011. Zbl1305.11032MR3011876

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