Multiple Dedekind zeta functions and evaluations of extended multiple zeta values
Multiple Dedekind zeta functions and evaluations of extended multiple zeta values
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多个 Dedekind zeta 函数和扩展的多个 zeta 值的评估
DOI：
10.1016/j.jnt.2004.12.010
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发表时间：
2005
影响因子：
0.7
通讯作者：
R. Masri
中科院分区：
文献类型：
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作者：
R. Masri
我们定义了Zagier在（First European Congress of Mathematics，vol. II（巴黎，1992），Progress in Mathematics，vol. 120，Birkhauser，巴塞尔，1994，pp. 497-512）。我们证明，在某些情况下，这个功能有一个亚纯继续镉，我们确定的线性子品种，包括它的奇点。我们使用我们的方法亚纯连续证明，存在无穷多个值的这些功能在其扩展域中的正规点，可以表示为一个合理的线性组合的Dedekind zeta函数的值。
We define the number field analog of the zeta function of d-complex variables studied by Zagier in (First European Congress of Mathematics, vol. II (Paris, 1992), Progress in Mathematics, vol. 120, Birkhauser, Basel, 1994, pp. 497–512). We prove that in certain cases this function has a meromorphic continuation to Cd, and we identify the linear subvarieties comprising its singularities. We use our approach to meromorphic continuation to prove that there exist infinitely many values of these functions at regular points in their extended domains which can be expressed as a rational linear combination of values of the Dedekind zeta function.