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A Shadow identity and an application to isoduality

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Abstract

The identity derived here from the theta transformation law replaces the “Atkin-Lehner identity” when the level decomposes into two factors which are not coprime. An application is given to the study of modular lattices of level 4, connected with modular forms for the classical theta group. CONWAY and Sloane have determined the maximal Hermite number of a self-dual lattice in ℝn for alln ≤ 33, and their result generalizes to the isodual case considered here in most of these dimensions.

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Correspondence to H. -G. Quebbemann.

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Quebbemann, H.-. A Shadow identity and an application to isoduality. Abh.Math.Semin.Univ.Hambg. 68, 339–345 (1998). https://doi.org/10.1007/BF02942571

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Keywords

  • Modular Form
  • Theta Function
  • Modular Lattice
  • Theta Series
  • Weight Enumerator