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Search: id:A108907
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| A108907 |
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Theta-series of unique unimodular lattice in dimension 26 with minimal norm 3. |
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1
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| 1, 0, 0, 3120, 102180, 1482624, 13191360, 83859360, 416587860, 1712638720, 6061945344, 19019791440, 54048571200, 141266958720, 343675612800, 786321725280, 1706284712340, 3532676509440, 7012626150400, 13413721342320, 24829712546184, 44601384921600
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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R. E. Borcherds, The Leech Lattice and Other Lattices, Ph. D. Dissertation, Cambridge Univ., 1984.
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, Third Ed., pp. xli-xlii.
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LINKS
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N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
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FORMULA
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Let f = theta_3, g = 8-dimensional cusp form [Conway-Sloane, p. 187, Eqs. (32)-(34)]. The theta-series is f^26 - 52*f^18*g + 156*f^10*g^2.
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EXAMPLE
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1 + 3120*q^3 + 102180*q^4 + 1482624*q^5 + 13191360*q^6 + 83859360*q^7 + 416587860*q^8 + ...
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CROSSREFS
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Sequence in context: A103523 A090056 A002433 this_sequence A107535 A133526 A102709
Adjacent sequences: A108904 A108905 A108906 this_sequence A108908 A108909 A108910
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KEYWORD
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nonn
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AUTHOR
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njas and Nadia Heninger (nadiah(AT)cs.princeton.edu), Jul 17 2005
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