Ramanujan J (2008) 16: 271–284 DOI 10.1007/s11139-007-9098-5 Identities of arithmetic type between values of the theta function associated to a lattice in R d and its derivatives Allal Ghanmi · Youssef Hantout · Ahmed Intissar · Changgui Zhang · Azzouz Zinoun Received: 23 June 2005 / Accepted: 12 December 2005 / Published online: 19 July 2008 © Springer Science+Business Media, LLC 2008 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 Mathematics Subject Classification (2000) Primary 14K25 · Secondary 33C15 1 Introduction and statement of main result Let θ Z (t) =  m∈Z e −tm 2 , t ∈ R > := (0, ∞) A. Ghanmi () · A. Intissar Department of Mathematics, Faculty of Sciences, P.O. Box: 1014, Mohammed V University—Agdal, 10 000 Rabat, Morocco e-mail: allalghanmi@gmail.com Y. Hantout · C. Zhang Laboratoire Paul Painlevé, UMR-CNRS 8524, UFR de Mathématiques, USTL, Cité Scientifique, 59655 Villeneuve d’Ascq Cedex, France A. Zinoun Laboratoire de Physique des Lasers, Atomes et Molécules, UMR-CNRS 8523, UFR de Physique, USTL, Cité Scientifique, 59655 Villeneuve d’Ascq, France