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On the representation of integers with large square factors by positive definite ternary quadratic forms
Author(s) -
Earnest A. G.
Publication year - 1984
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/s002557930001247x
Subject(s) - mathematics , positive definite matrix , ternary operation , square free integer , combinatorics , genus , integer (computer science) , discriminant , quadratic integer , spinor , quadratic form (statistics) , binary quadratic form , quadratic equation , discrete mathematics , quadratic function , mathematical analysis , mathematical physics , algebraic number , eigenvalues and eigenvectors , physics , botany , geometry , quantum mechanics , artificial intelligence , computer science , biology , programming language
It is proved here that, if G is a positive definite integral ternary quadratic lattice of discriminant d and c is a squarefree integer which is primitively represented by the genus of G , then G primitively represents all sufficiently large integers of the type ct 2 , with g.c.d. ( t , 2 d ) = 1, which are primitively represented by the spinor genus of G .