CPL - Chalmers Publication Library
| Utbildning | Forskning | Styrkeområden | Om Chalmers | In English In English Ej inloggad.

Almost holomorphic Poincare series corresponding to products of harmonic Siegel-Maass forms

Kathrin Bringmann ; Olav K. Richter ; Martin Westerholt-Raum (Institutionen för matematiska vetenskaper, Algebra och geometri)
RESEARCH IN THE MATHEMATICAL SCIENCES (2197-9847). Vol. 3 (2016), p. Art. no. 30.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: degenerate principal series, modular-forms, representations, conjecture



Denna post skapades 2017-12-28.
CPL Pubid: 254115

 

Läs direkt!


Länk till annan sajt (kan kräva inloggning)


Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, Algebra och geometriInstitutionen för matematiska vetenskaper, Algebra och geometri (GU)

Ämnesområden

Matematik

Chalmers infrastruktur