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<p>The product formula for the measure of representations of a quadratic form over the rational number field was found by Siegel, and were generalized by Fractman to the higher-dimensional case over totally real algebraic number fields. We prove product formulas for quadratic forms over arbitrary algebraic number fields and generalize formulas given by Siegel and Fractman to the case of arbitrary algebraic number fields.</p>

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On Siegel’s product formulas for quadratic forms over algebraic number fields in higher dimensional cases

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月16日

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  • Hisashi Kojima,
  • Hiroshi Sakata

摘要

The product formula for the measure of representations of a quadratic form over the rational number field was found by Siegel, and were generalized by Fractman to the higher-dimensional case over totally real algebraic number fields. We prove product formulas for quadratic forms over arbitrary algebraic number fields and generalize formulas given by Siegel and Fractman to the case of arbitrary algebraic number fields.