# Higher order invariants in the case of compact quotients

Open Mathematics (2011)

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

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topAnton 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

top- [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] 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] Deitmar A., Higher order group cohomology and the Eichler-Shimura map, J. Reine Angew. Math., 2009, 629, 221–235 Zbl1254.11051
- [4] Deitmar A., Higher order invariants, cohomology, and automorphic forms, preprint available at http://arxiv.org/abs/0811.1088 Zbl06116927
- [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] Deitmar A., Echterhoff S., Principles of Harmonic Analysis, Universitext, Springer, New York, 2009 Zbl1158.43001
- [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] 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] Diamantis N., Sim D., The classification of higher-order cusp forms, J. Reine Angew. Math., 2008, 622, 121–153 Zbl1230.11049
- [10] Farmer D., Converse theorems and second order modular forms, AMS Sectional Meeting, Salt Lake City, October 26–27, 2002
- [11] Feldman J., Greenleaf F.P., Existence of Borel transversals in groups, Pacific J. Math., 1968, 25(3), 455–461 Zbl0159.31703
- [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] 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] 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] 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] 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] 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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