Zonal functions for the unitary groups and applications to Hermitian lattices.

DOI10.1006/jnth.2002.2785zbMath1046.11050OpenAlexW2067728005MaRDI QIDQ1864848

Gabriele Nebe, Christine Bachoc

Publication date: 23 March 2003

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.2002.2785

zbMATH Keywords

latticeunitary grouptheta serieszonal spherical function

Mathematics Subject Classification ID

Lattices and convex bodies (number-theoretic aspects) (11H06) Theta series; Weil representation; theta correspondences (11F27) Spherical harmonics (33C55)

Related Items (2)

Designs, groups and lattices ⋮ Codes over $\mathbf {GF\pmb (4\pmb )}$ and $\mathbf {F}_2 \times \mathbf {F}_2$ and Hermitian lattices over imaginary quadratic fields

Cites Work

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• t-designs in projective spaces
• The theory of Jacobi forms
• On even unimodular extremal lattices
• On automorphic forms on the unitary symplectic group \(\mathrm{Sp}(n)\) and \(\mathrm{SL}_ 2(\mathbb R)\)
• Finite quaternionic reflection groups
• Spherical codes and designs
• Some lattices over \(Q(\sqrt{-3})^*\)
• Self-dual codes over GF(4)
• Classification of Hermitian forms with the neighbour method
• Atkin-Lehner eigenforms and strongly modular lattices
• Modular lattices in Euclidean spaces
• Neighborhood in the sense of Kneser for quaternionic lattices
• Finite Subgroups of GL₂4(Q)
• The root lattices of the complex reflection groups
• Classification of Two Genera of 32-Dimensional Lattices of Rank 8 over the Hurwitz Order
• Classification of integral lattices with large class number
• Finite Unitary Reflection Groups

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