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2011 | 9 | 1 | 85-101
Tytuł artykułu

Higher order invariants in the case of compact quotients

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
1
Strony
85-101
Opis fizyczny
Daty
wydano
2011-02-01
online
2010-12-30
Twórcy
Bibliografia
  • [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
  • [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
  • [3] Deitmar A., Higher order group cohomology and the Eichler-Shimura map, J. Reine Angew. Math., 2009, 629, 221–235
  • [4] Deitmar A., Higher order invariants, cohomology, and automorphic forms, preprint available at http://arxiv.org/abs/0811.1088
  • [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
  • [6] Deitmar A., Echterhoff S., Principles of Harmonic Analysis, Universitext, Springer, New York, 2009
  • [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
  • [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
  • [9] Diamantis N., Sim D., The classification of higher-order cusp forms, J. Reine Angew. Math., 2008, 622, 121–153
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-010-0081-9
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