The fifteen theorem, and generalizations
Bhargava, Manjul
(2001)
The fifteen theorem, and generalizations.
In: Robert J. Bumcrot Festschrift, 11 May 2001, Hofstra University.
Full text available as: AbstractThe classical "Four Squares Theorem" of Lagrange asserts that any positive integer can be expressed as the sum of four squares; that is, the quadratic form a2 + b2 + c2 + d2 represents all (positive) integers. When does a general quadratic form represent all integers? When does it represent all odd integers? When does it represent all primes? We show how all these questions turn out to have very simple and surprising answers. | Item Type: | Conference or Workshop Item (Paper) |
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| Additional Information: | This paper was given at the Robert J. Bumcrot Festschrift on May 11, 2001 |
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| Uncontrolled Keywords: | The classical "Four Squares Theorem" of Lagrange asserts that any positive integer can be expressed as the sum of four squares; that is, the quadratic form a2 + b2 + c2 + d2 represents all (positive) integers. When does a general quadratic form represent all integers? When does it represent all odd integers? When does it represent all primes? We show how all these questions turn out to have very simple and surprising answers. |
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| Subjects: | Q Science > Q Science (General)
Q Science > QA Mathematics |
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| ID Code: | 24 |
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| Deposited By: | Admin HofPrints |
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| Deposited On: | 03 January 2006 |
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