Definability of arithmetical operations from binary quadratic forms

Ivan Korec

Displaying similar documents to “Definability of arithmetical operations from binary quadratic forms”

The genera representing a positive integer

Pierre Kaplan, Kenneth S. Williams (2002)

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The inhomogeneous minimum of quadratic forms of signature zero

B. Birch (1958)

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On Bailey pairs and certain q-series related to quadratic and ternary quadratic forms

Alexander E. Patkowski (2011)

Colloquium Mathematicae

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We provide a new approach to establishing certain q-series identities that were proved by Andrews, and show how to prove further identities using conjugate Bailey pairs. Some relations between some q-series and ternary quadratic forms are established.

Note to the Paper "A Positive Definite Binary Quadratic Form as a Sum of Five Squares of Linear Forms (Completion of Mordell's Proof)" (Bull. Polish Acad. Sci. Math. 61 (2013), 23-26)

A. Schinzel (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

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The Diophantine equation $x y + y z + x z = n$ and indecomposable binary quadratic forms.

Peters, Meinhard (2004)

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Binary quadratic forms and sums of triangular numbers

Zhi-Hong Sun (2011)

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A Positive Definite Binary Quadratic Form as a Sum of Five Squares of Linear Forms (Completion of Mordell's Proof)

A. Schinzel (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

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The paper completes an incomplete proof given by L. J. Mordell in 1930 of the following theorem: every positive definite classical binary quadratic form is the sum of five squares of linear forms with integral coefficients.

Ternary quadratic forms ax² + by² + cz² representing all positive integers 8k + 4

Kenneth S. Williams (2014)

Acta Arithmetica

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Under the assumption that the ternary form x² + 2y² + 5z² + xz represents all odd positive integers, we prove that a ternary quadratic form ax² + by² + cz² (a,b,c ∈ ℕ) represents all positive integers n ≡ 4(mod 8) if and only if it represents the eight integers 4,12,20,28,52,60,140 and 308.