Higher order invariants in the case of compact quotients

• Autorzy: Anton Deitmar
• 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

EN

Automorphic forms; Higher order

Kategorie tematyczne

• 11F55: Other groups and their modular and automorphic forms (several variables)
• 11F75: Cohomology of arithmetic groups

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 1
• Strony: 85-101

Daty

wydano

2011-02-01

online

2010-12-30

Twórcy

autor

Anton Deitmar

• Mathematisches Institut

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

Identyfikatory

DOI

10.2478/s11533-010-0081-9