Gun, Sanoli ; Oesterlé, Joseph (2015) The circle method and non-lacunarity of meromorphic modular forms Journal fur die reine und angewandte Mathematik, 2015 (703). pp. 1-25. ISSN 0075-4102
Full text not available from this repository.
Official URL: http://doi.org/10.1515/crelle-2013-0046
Related URL: http://dx.doi.org/10.1515/crelle-2013-0046
Abstract
Serre proved that any holomorphic cusp form of weight one forÄ1.N/is la-cunary while a holomorphic modular form forÄ1.N/of higher integer weight is lacunary ifand only if it is a linear combination of cusp forms of CM-type (see [Publ. Math. I.H.E.S. 54(1981), 323–401, Sections 7.6 and 7.7]). In this paper, we show that when a non-zero mero-morphic modular form of arbitrary real weight for any finite index subgroup of the modulargroup SL2.Z/is lacunary, it is necessarily holomorphic on the upper-half plane, finite at thecusps and has non-negative weight.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Walter de Gruyter GmbH. |
| ID Code: | 118032 |
| Deposited On: | 11 May 2021 11:27 |
| Last Modified: | 11 May 2021 11:27 |
Repository Staff Only: item control page
