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Classes of integral 3‐tensors on 2‐space
Author(s) -
Kable Anthony C.
Publication year - 2000
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300015825
Subject(s) - mathematics , discriminant , rank (graph theory) , pure mathematics , class (philosophy) , space (punctuation) , action (physics) , quadratic equation , combinatorics , algebra over a field , geometry , linguistics , philosophy , physics , quantum mechanics , artificial intelligence , computer science
The space of integral 3‐tensors isℤ 2 ⊗ ℤ 2 ⊗ ℤ 2under the standard action ofSL 2 ( ℤ ) × SL 2 ( ℤ ) × SL 2 ( ℤ ) . A notion of primitivity is defined in this space and the number of primitive classes of a given discriminant is evaluated in terms of the class number of primitive binary quadratic forms of the same discriminant. Classes containing symmetric 3‐tensors are also considered and their number is related to the 3‐rank of the class group.