Jha, Abhash Kumar and Kumar, Arvind (2017) Construction of Cusp Forms Using Rankin–Cohen Brackets. In: International Gainesville Number Theory Conference in Honor of Krishna Alladi’s 60th Birthday, 2016, 17 March - 21 March 2016, Gainesville, pp. 329-341.
Full text not available from this repository.Abstract
For a fixed modular form we consider a family of linear maps constructed using Rankin–Cohen brackets. We explicitly compute the adjoint of these maps with respect to the Petersson scalar product. The Fourier coefficients of the image of a cusp form under the adjoint maps are, up to a constant, a special value of a certain shifted Rankin–Selberg convolution attached to them. This is a generalization of the work due to Kohnen (Math. Z. 207 (1991), 657–660) and Herrero (Ramanujan J. 36 (2014), no. 3, 529–536) in the case of integral weight modular forms to half-integral weight modular forms. As a consequence we get non-vanishing and asymptotic bound for the special values of a certain shifted Rankin–Selberg convolution of modular forms.
| Item Type: | Conference Proceedings |
|---|---|
| Series.: | Springer Proceedings in Mathematics & Statistics |
| Publisher: | Springer New York LLC |
| Additional Information: | The Copyright of this article belong to the Authors |
| Keywords: | Adjoint map; Dirichlet series; Modular forms; Rankin–Cohen brackets; Convolution; Fourier analysis; Number theory; Adjoints; Asymptotic bounds; Dirichlet series; Fourier coefficients; Linear maps; Modular forms; Scalar product; Fasteners |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 25 May 2022 05:04 |
| Last Modified: | 25 May 2022 05:04 |
| URI: | https://eprints.iisc.ac.in/id/eprint/72607 |
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