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Primitive Representations by Spinor Genera of Ternary Quadratic Forms
Author(s) -
Earnest A. G.,
Hsia J. S.,
Hung D. C.
Publication year - 1994
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/50.2.222
Subject(s) - mathematics , genus , spinor , ternary operation , multiplicative function , ring of integers , combinatorics , prime (order theory) , algebraic number , pure mathematics , discrete mathematics , algebraic number field , mathematical physics , zoology , mathematical analysis , computer science , biology , programming language
Let a be primitively represented by the genus of a ternary quadratic lattice L defined over the ring of integers of an algebraic number field F . Criteria to determine whether a is primitively represented by every spinor genus in the genus of L involve certain subgroups θ∗( L p , a ) of the multiplicative groups of the localizations F p of F with respect to the various nonarchimedean prime spots p on F . In this paper these groups θ∗( L p , a ) are determined explicitly for nondyadic and 2‐adic prime spots. Examples are given which show how this information can, in some instances, be used in combination with known results, to determine all integers primitively represented by a particular positive definite ternary quadratic form.