On the existence of singular solutions.
Bartušek, M., Osička, J. (2001)
Georgian Mathematical Journal
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Bartušek, M., Osička, J. (2001)
Georgian Mathematical Journal
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El-Sayed, A.M.A., Hashem, H.H.G. (2009)
The Journal of Nonlinear Sciences and its Applications
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Aloys Krieg (1993)
Acta Arithmetica
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The main purpose of the reduction theory is to construct a fundamental domain of the unimodular group acting discontinuously on the space of positive definite quadratic forms. This fundamental domain is for example used in the theory of automorphic forms for GLₙ (cf. [11]) or in the theory of Siegel modular forms (cf. [1], [4]). There are several ways of reduction, which are usually based on various minima of the quadratic form, e.g. the Korkin-Zolotarev method (cf. [10], [3]),...
Jürgen Eichenauer-Herrmann, Harald Niederreiter (1995)
Acta Arithmetica
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William C. Jagy (1996)
Acta Arithmetica
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1. Introduction. In a recent article [6], the positive definite ternary quadratic forms that can possibly represent all odd positive integers were found. There are only twenty-three such forms (up to equivalence). Of these, the first nineteen were proven to represent all odd numbers. The next four are listed as "candidates". The aim of the present paper is to show that one of the candidate forms h = x² + 3y² + 11z² + xy + 7yz does represent all odd (positive) integers, and that it is...
Irving Kaplansky (1995)
Acta Arithmetica
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Peter Schmid (1999)
Acta Arithmetica
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Bartušek, Miroslav (2006)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Jeffrey Stopple (1995)
Acta Arithmetica
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