Higher order invariants in the case of compact quotients

Anton Deitmar

Open Mathematics (2011)

  • Volume: 9, Issue: 1, page 85-101
  • ISSN: 2391-5455

Abstract

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We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case, many things simplify and we are thus able to prove a more precise structure theorem than in the general case.

How to cite

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Anton Deitmar. "Higher order invariants in the case of compact quotients." Open Mathematics 9.1 (2011): 85-101. <http://eudml.org/doc/269731>.

@article{AntonDeitmar2011,
abstract = {We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case, many things simplify and we are thus able to prove a more precise structure theorem than in the general case.},
author = {Anton Deitmar},
journal = {Open Mathematics},
keywords = {Automorphic forms; Higher order; automorphic forms; higher order; compact quotient},
language = {eng},
number = {1},
pages = {85-101},
title = {Higher order invariants in the case of compact quotients},
url = {http://eudml.org/doc/269731},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Anton Deitmar
TI - Higher order invariants in the case of compact quotients
JO - Open Mathematics
PY - 2011
VL - 9
IS - 1
SP - 85
EP - 101
AB - We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case, many things simplify and we are thus able to prove a more precise structure theorem than in the general case.
LA - eng
KW - Automorphic forms; Higher order; automorphic forms; higher order; compact quotient
UR - http://eudml.org/doc/269731
ER -

References

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  1. [1] Borel A., Wallach N.R., Continuous Cohomology, Discrete Groups, and Representations of Reductive Groups, Ann. of Math. Stud., 94, Princeton University Press, Princeton, 1980 Zbl0443.22010
  2. [2] Chinta G., Diamantis N., O'sullivan C., Second order modular forms, Acta Arith., 2002, 103(3), 209–223 http://dx.doi.org/10.4064/aa103-3-2 Zbl1020.11025
  3. [3] Deitmar A., Higher order group cohomology and the Eichler-Shimura map, J. Reine Angew. Math., 2009, 629, 221–235 Zbl1254.11051
  4. [4] Deitmar A., Higher order invariants, cohomology, and automorphic forms, preprint available at http://arxiv.org/abs/0811.1088 Zbl06116927
  5. [5] Deitmar A., Diamantis N., Automorphic forms of higher order, J. Lond. Math. Soc., 2009, 80(1), 18–34 http://dx.doi.org/10.1112/jlms/jdp015 Zbl1239.11052
  6. [6] Deitmar A., Echterhoff S., Principles of Harmonic Analysis, Universitext, Springer, New York, 2009 Zbl1158.43001
  7. [7] Diamantis N., Knopp M., Mason G., O'sullivan C., L-functions of second-order cusp forms, Ramanujan J., 2006, 12(3), 327–347 http://dx.doi.org/10.1007/s11139-006-0147-2 Zbl1198.11048
  8. [8] Diamantis N., O'sullivan C., The dimensions of spaces of holomorphic second-order automorphic forms and their cohomology, Trans. Amer. Math. Soc., 2008, 360(11), 5629–5666 http://dx.doi.org/10.1090/S0002-9947-08-04755-7 Zbl1158.11021
  9. [9] Diamantis N., Sim D., The classification of higher-order cusp forms, J. Reine Angew. Math., 2008, 622, 121–153 Zbl1230.11049
  10. [10] Farmer D., Converse theorems and second order modular forms, AMS Sectional Meeting, Salt Lake City, October 26–27, 2002 
  11. [11] Feldman J., Greenleaf F.P., Existence of Borel transversals in groups, Pacific J. Math., 1968, 25(3), 455–461 Zbl0159.31703
  12. [12] Goldfeld D., Modular forms, elliptic curves and the ABC-conjecture, In: A Panorama of Number Theory or the View from Baker's Garden, Zürich, 1999, Cambridge University Press, Cambridge, 2002, 128–147 http://dx.doi.org/10.1017/CBO9780511542961.010 
  13. [13] Goldfeld D., Gunnells P.E., Eisenstein series twisted by modular symbols for the group SLn, Math. Res. Lett., 2000, 7(5–6), 747–756 Zbl1002.11043
  14. [14] Imamoḡlu Ö., Martin Y., A converse theorem for second-order modular forms of level N, Acta Arith., 2006, 123(4), 361–376 http://dx.doi.org/10.4064/aa123-4-5 Zbl1165.11050
  15. [15] Imamoḡlu Ö., O'sullivan C., Parabolic, hyperbolic and elliptic Poincaré series, Acta Arith., 2009, 139(3), 199–228 http://dx.doi.org/10.4064/aa139-3-1 Zbl1279.11041
  16. [16] Kleban P., Zagier D., Crossing probabilities and modular forms, J. Statist. Phys., 2003, 113(3–4), 431–454 http://dx.doi.org/10.1023/A:1026012600583 Zbl1081.60067
  17. [17] Schwermer J., Cohomology of arithmetic groups, automorphic forms and L-functions, In: Cohomology of Arithmetic Groups and Automorphic Forms, Luminy-Marseille, 1989, Lecture Notes in Math., 1447, Springer, Berlin, 1990, 1–29 http://dx.doi.org/10.1007/BFb0085724 

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