On some results of Hurwitz and Deutsch about certain quadratic forms

Bumkyu Cho; Ho Park

doi:10.1016/j.jnt.2014.04.016

On some results of Hurwitz and Deutsch about certain quadratic forms

Bumkyu Cho, Ho Park

Department of Mathematics

Dongguk University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this paper we introduce some results of Hurwitz and Deutsch about the number of representations of integers by quadratic forms x2+y2+z2+w2 and x2+y2+2z2+2w2 with certain parity conditions on the variables x, y, z and w. The purpose of this paper is to provide another proof of these results by the use of Liouville type identities, and see how many more similar results can be shown with this technique.

Original language	English
Pages (from-to)	1-14
Number of pages	14
Journal	Journal of Number Theory
Volume	144
DOIs	https://doi.org/10.1016/j.jnt.2014.04.016
State	Published - Nov 2014

Keywords

Liouville identities
Number of representations
Quadratic forms

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10.1016/j.jnt.2014.04.016

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abstract = "In this paper we introduce some results of Hurwitz and Deutsch about the number of representations of integers by quadratic forms x2+y2+z2+w2 and x2+y2+2z2+2w2 with certain parity conditions on the variables x, y, z and w. The purpose of this paper is to provide another proof of these results by the use of Liouville type identities, and see how many more similar results can be shown with this technique.",

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AB - In this paper we introduce some results of Hurwitz and Deutsch about the number of representations of integers by quadratic forms x2+y2+z2+w2 and x2+y2+2z2+2w2 with certain parity conditions on the variables x, y, z and w. The purpose of this paper is to provide another proof of these results by the use of Liouville type identities, and see how many more similar results can be shown with this technique.

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KW - Number of representations

KW - Quadratic forms

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JO - Journal of Number Theory

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ER -

On some results of Hurwitz and Deutsch about certain quadratic forms

Abstract

Keywords

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