Fourier expansions of complex-valued Eisenstein series on finite upper half planes
We consider complex-valued modular forms on finite upper half planes Hq and obtain Fourier expansions of Eisenstein series invariant under the groups Γ=SL(2,Fp) and GL(2,Fp). The expansions are analogous to those of Maass wave forms on the ordinary Poincaré upper half plane —the K-Bessel functions...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/63918 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832558297083805696 |
|---|---|
| author | Anthony Shaheen Audrey Terras |
| author_facet | Anthony Shaheen Audrey Terras |
| author_sort | Anthony Shaheen |
| collection | DOAJ |
| description | We consider complex-valued modular forms on finite upper half planes Hq and obtain Fourier expansions of Eisenstein series invariant under the groups
Γ=SL(2,Fp)
and GL(2,Fp). The expansions are analogous to those of Maass wave forms on the ordinary Poincaré upper half plane —the K-Bessel functions being replaced by Kloosterman sums. |
| format | Article |
| id | doaj-art-1be9546b43bb4625b3ea36898d72ddc1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1be9546b43bb4625b3ea36898d72ddc12025-02-03T01:32:45ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/6391863918Fourier expansions of complex-valued Eisenstein series on finite upper half planesAnthony Shaheen0Audrey Terras1Department of Mathematics, California State University, Los Angeles 90032-8204, CA, USADepartment of Mathematics, University of California, San Diego, La Jolla 92093-0112, CA, USAWe consider complex-valued modular forms on finite upper half planes Hq and obtain Fourier expansions of Eisenstein series invariant under the groups Γ=SL(2,Fp) and GL(2,Fp). The expansions are analogous to those of Maass wave forms on the ordinary Poincaré upper half plane —the K-Bessel functions being replaced by Kloosterman sums.http://dx.doi.org/10.1155/IJMMS/2006/63918 |
| spellingShingle | Anthony Shaheen Audrey Terras Fourier expansions of complex-valued Eisenstein series on finite upper half planes International Journal of Mathematics and Mathematical Sciences |
| title | Fourier expansions of complex-valued Eisenstein series on finite
upper half planes |
| title_full | Fourier expansions of complex-valued Eisenstein series on finite
upper half planes |
| title_fullStr | Fourier expansions of complex-valued Eisenstein series on finite
upper half planes |
| title_full_unstemmed | Fourier expansions of complex-valued Eisenstein series on finite
upper half planes |
| title_short | Fourier expansions of complex-valued Eisenstein series on finite
upper half planes |
| title_sort | fourier expansions of complex valued eisenstein series on finite upper half planes |
| url | http://dx.doi.org/10.1155/IJMMS/2006/63918 |
| work_keys_str_mv | AT anthonyshaheen fourierexpansionsofcomplexvaluedeisensteinseriesonfiniteupperhalfplanes AT audreyterras fourierexpansionsofcomplexvaluedeisensteinseriesonfiniteupperhalfplanes |