On the integrality of \(n\)th roots of generating functions

DOI10.1016/j.jcta.2006.03.018zbMath1203.94138arXivmath/0509316OpenAlexW1581066001WikidataQ60692207 ScholiaQ60692207MaRDI QIDQ855873

N. J. A. Sloane, Nadia Heninger, Eric M. Rains

Publication date: 7 December 2006

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0509316

zbMATH Keywords

fractional powersBCH codesinteger sequencestheta seriesLeech latticeformal power seriesKerdock codes\(E_8\) latticePreparata codesBarnes--Wall latticesReed--Muller codessquare roots of seriesWeight enumerators

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Theta series; Weil representation; theta correspondences (11F27) Combinatorial codes (94B25) Relations with coding theory (11H71)

Related Items

On Dwork’s 𝑝-adic formal congruences theorem and hypergeometric mirror maps ⋮ On the integrality of the Taylor coefficients of mirror maps ⋮ The partition-frequency enumeration matrix ⋮ Nonlinear differential equations satisfied by certain classical modular forms ⋮ Integrality of the Taylor coefficients of roots of mirror maps ⋮ Arithmetic properties of Picard-Fuchs equations and holonomic recurrences ⋮ ON EXTREMAL QUASI-MODULAR FORMS AFTER KANEKO AND KOIKE

Uses Software

• Maple
• OEIS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The automorphism group of an [18,9,8 quaternary code]
• Upper bounds for modular forms, lattices, and codes
• Self-dual codes over GF(4)
• A note on optimal unimodular lattices
• Some cyclo-quaternionic lattices
• Modular lattices in Euclidean spaces
• Theq—-series of monstrous moonshine & the decomposition of the head characters
• On the weight enumeration of weights less than 2.5d of Reed—Muller codes
• Extremal self‐dual lattices exist only in dimensions 1 to 8, 12, 14, 15, 23, and 24
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• More on replicable functions
• Codes and invariant theory
• The weight distribution of the third-order Reed-Muller code of length 512
• Weight enumerator for second-order Reed-Muller codes
• A (48, 31, 8) linear code (Corresp.)
• \(p\)-adic numbers. An introduction
• On unique factorization domains
• Coding theory