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Positive definite almost regular ternary quadratic forms over totally real number fields
Author(s) -
Chan Wai Kiu,
Icaza Maria Ines
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn085
Subject(s) - mathematics , positive definite matrix , ternary operation , integer (computer science) , quadratic form (statistics) , combinatorics , definite quadratic form , binary quadratic form , quadratic equation , quadratic field , real number , field (mathematics) , algebraic number field , discrete mathematics , pure mathematics , quadratic function , geometry , eigenvalues and eigenvectors , physics , quantum mechanics , computer science , programming language
Let F be a totally real number field and let be the ring of integers in F . A totally positive quadratic form f over is said to be almost regular with k exceptions if f represents all but k elements in F that are represented by f locally everywhere. In this paper, we show that for a fixed positive integer k , there are only finitely many similarity classes of positive definite almost regular ternary quadratic forms over with at most k exceptions. This generalizes the corresponding finiteness result for positive definite ternary quadratic forms over ℤ by Watson (PhD Thesis, University College, London, 1953; Mathematika 1 (1954) 104–110).