Sökning: id:"swepub:oai:gup.ub.gu.se/259511" >
Almost holomorphic ...
Almost holomorphic Poincaré series corresponding to products of harmonic Siegel-Maass forms
-
- Bringmann, K. (författare)
- Universität zu Köln,University of Cologne
-
- Richter, O. K. (författare)
- University of North Texas
-
- Westerholt-Raum, Martin, 1985 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology
-
(creator_code:org_t)
- 2016-12-10
- 2016
- Engelska.
-
Ingår i: Research in the Mathematical Sciences. - : Springer Science and Business Media LLC. - 2197-9847 .- 2522-0144. ; 3
- Relaterad länk:
-
https://link.springe...
-
visa fler...
-
https://research.cha... (primary) (free)
-
https://gup.ub.gu.se...
-
https://doi.org/10.1...
-
https://research.cha...
-
visa färre...
Abstract
Ämnesord
Stäng
- We investigate Poincare series, where we average products of terms of Fourier series of real-analytic Siegel modular forms. There are some (trivial) special cases for which the products of terms of Fourier series of elliptic modular forms and harmonic Maass forms are almost holomorphic, in which case the corresponding Poincare series are almost holomorphic as well. In general, this is not the case. The main point of this paper is the study of Siegel-Poincare series of degree 2 attached to products of terms of Fourier series of harmonic Siegel-Maass forms and holomorphic Siegel modular forms. We establish conditions on the convergence and nonvanishing of such Siegel-Poincare series. We surprisingly discover that these Poincare series are almost holomorphic Siegel modular forms, although the product of terms of Fourier series of harmonic Siegel-Maass forms and holomorphic Siegel modular forms (in contrast to the elliptic case) is not almost holomorphic. Our proof employs tools from representation theory. In particular, we determine some constituents of the tensor product of Harish-Chandra modules with walls.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
- NATURVETENSKAP -- Matematik -- Geometri (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Geometry (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- Almost holomorphic modular forms
- Siegel modular forms
- Harish-Chandra modules
- degenerate principal series
- modular-forms
- representations
- conjecture
- Harish-Chandra modules
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
Hitta via bibliotek
Till lärosätets databas