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Identities of arithmetic type between values of the theta function associated to a lattice in ? d and its derivatives |
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| Authors: | Allal Ghanmi Youssef Hantout Ahmed Intissar Changgui Zhang Azzouz Zinoun |
| Institution: | (1) Department of Mathematics, Faculty of Sciences, Mohammed V University—Agdal, P.O. Box: 1014, 10 000 Rabat, Morocco;(2) Laboratoire Paul Painlevé, UMR-CNRS 8524, UFR de Mathématiques, USTL, Cité Scientifique, 59655 Villeneuve d’Ascq Cedex, France;(3) Laboratoire de Physique des Lasers, Atomes et Molécules, UMR-CNRS 8523, UFR de Physique, USTL, Cité Scientifique, 59655 Villeneuve d’Ascq, France |
| Abstract: | In this paper, we introduce a notion of similarly self dual lattice in a d-dimensional Euclidean space and a classical Jacobi theta function is associated to such a lattice. We establish identities of arithmetic type between values of this theta function and its successive derivatives. This work can be related to the spectral theory of the Landau operators. |
| Keywords: | Dual lattice Similarly self dual lattice Poisson summation formula Theta functions Confluent hypergeometrique function |
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