Note on almost-universal forms
About: This article is published in Bulletin of the American Mathematical Society. The article was published on 01 Feb 1938. and is currently open access.
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Citations
Classically integral quadratic forms excepting at most two values
Madeleine Barowsky,William Damron,Andres Mejia,Frederick Saia,Nolan Schock,Katherine Thompson +5 more
- 01 Jun 2018
TL;DR: In this paper, it was shown that there is no positive definite quadratic form that fails to represent all positive integers except for five elements of a quaternary form except for the elements of the elements in the form of four squares.
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•Journal Article
GoNII: Universal Quaternary Quadratic Forms.
TL;DR: A small multiple theorem is given and used to prove universality for all nine universal diagonal forms of square discriminant in x2+2y2+5z2+10w2, which required computer calculations.
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The representation of quadratic forms by almost universal forms of higher rank
TL;DR: In this article, it was shown that there are only finitely many positive definite integral quadratic forms of rank n+3(n≥2) that represent all positive definite quadrastic forms of the rank n, but with only a finite number of exceptions.
A “Four Integers” Theorem and a “Five Integers” Theorem
TL;DR: Two results of this type for positive diagonal ternary forms for positive integral quadratic forms in any number of variables are proved and the “four integers” and "five integers" theorems of the title are proved.