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Identities of arithmetic type between values of the theta function associated to a lattice in ℝd and its derivatives

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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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Mohammed V University—Agdal, P.O. Box: 1014, 10 000, Rabat, Morocco

    Allal Ghanmi & Ahmed Intissar

  2. Laboratoire Paul Painlevé, UMR-CNRS 8524, UFR de Mathématiques, USTL, Cité Scientifique, 59655, Villeneuve d’Ascq Cedex, France

    Youssef Hantout & Changgui Zhang

  3. Laboratoire de Physique des Lasers, Atomes et Molécules, UMR-CNRS 8523, UFR de Physique, USTL, Cité Scientifique, 59655, Villeneuve d’Ascq, France

    Azzouz Zinoun

Authors
  1. Allal Ghanmi
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  2. Youssef Hantout
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  3. Ahmed Intissar
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  4. Changgui Zhang
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  5. Azzouz Zinoun
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Correspondence to Allal Ghanmi.

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Ghanmi, A., Hantout, Y., Intissar, A. et al. Identities of arithmetic type between values of the theta function associated to a lattice in ℝd and its derivatives. Ramanujan J 16, 271–284 (2008). https://doi.org/10.1007/s11139-007-9098-5

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  • DOI: https://doi.org/10.1007/s11139-007-9098-5

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