On a Certain Integral Over a Triangle
英文摘要:
We study integrals over the triangle with vertices (1,0), (0,1), (1,1) that give linear combinations of multiple zeta values.
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Sergey Zlobin
We study integrals over the triangle with vertices (1,0), (0,1), (1,1) that give linear combinations of multiple zeta values.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
继续探索
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该研究通过椭圆曲线理论证明存在无限多个原始海伦三角形,其中两边为完全平方数,并暗示可能存在三边均为完全平方数的原始海伦三角形。
A rational triangle is a triangle with rational sides and rational area. A Heron triangle is a triangle with integral sides and integral area. In this article we will show that there exist infinitely many rational parametrizations, in terms of s, of rational triangles with perimeter 2s(s+1) and area s(s^2-1). As a corollary, there exist arbitrarily many Heron triangles with all the same area and the same perimeter. The proof uses an elliptic K3 surface Y. Its Picard number is computed to be 18 after we prove that the Neron-Severi group of Y injects naturally into the Neron-Severi group of the …
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本文基于Hayes定理,对PGL₂(ℚ)上某1-上循环在s=0处的特殊值给出几何解释,并由此得到上循环显式公式、Hayes定理的推广与新证明,以及ℝ²中三角形Ehrhart拟多项式零次系数的求和公式。
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