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Forms representing forms: the definite case
Author(s) -
Brandes Julia
Publication year - 2015
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/jdv028
Subject(s) - mathematics , hypersurface , definite quadratic form , positive definite matrix , degree (music) , quadratic form (statistics) , combinatorics , pure mathematics , quadratic equation , quadratic function , binary quadratic form , eigenvalues and eigenvectors , geometry , physics , quantum mechanics , acoustics
Let ψ and F be positive‐definite forms with integral coefficients of equal degree. Using the circle method, we establish an asymptotic formula for the number of identical representations of ψ by F , provided that ψ is everywhere locally representable and the number of variables of F is large enough. In the quadratic case, this supersedes a recent result due to Dietmann and Harvey. Another application addresses the number of primitive linear spaces contained in a hypersurface.