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July, 2018 On the solutions of quadratic Diophantine equations II
Manabu MURATA, Takashi YOSHINAGA
J. Math. Soc. Japan 70(3): 895-919 (July, 2018). DOI: 10.2969/jmsj/76747674

Abstract

A quantity concerning the solutions of a quadratic Diophantine equation in $n$ variables coincides with a mass of a special orthogonal group of a quadratic form in dimension $n-1$, via the mass formula due to Shimura. We show an explicit formula for the quantity, assuming the maximality of a lattice in the $(n-1)$-dimensional quadratic space. The quantity is determined by the computation of a group index and of the mass of the genus of maximal lattices in that quadratic space. As applications of the result, we give the number of primitive solutions for the sum of $n$ squares with 6 or 8 and also the quantity in question for the sum of 10 squares.

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Manabu MURATA. Takashi YOSHINAGA. "On the solutions of quadratic Diophantine equations II." J. Math. Soc. Japan 70 (3) 895 - 919, July, 2018. https://doi.org/10.2969/jmsj/76747674

Information

Received: 25 November 2016; Published: July, 2018
First available in Project Euclid: 18 June 2018

zbMATH: 06966966
MathSciNet: MR3830791
Digital Object Identifier: 10.2969/jmsj/76747674

Subjects:
Primary: 11D09
Secondary: 11D45, 11E12

Rights: Copyright © 2018 Mathematical Society of Japan

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Vol.70 • No. 3 • July, 2018
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