Power sums with applications to multizeta and zeta zero distribution for Fq[t]
Power sums with applications to multizeta and zeta zero distribution for Fq[t]
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Fq[t] 的 multizeta 和 zeta 零分布的幂和应用
DOI：
10.1016/j.ffa.2009.04.002
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
D. Thakur
中科院分区：
文献类型：
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作者：
D. Thakur
研究有限域上给定次数的一元多项式的整幂和。取消的组合学是相当复杂的。我们证明了几个结果的程度，这些和直接或递归公式，同余条件和程度界。我们指出了一个“二重性”的价值观之间的积极和消极的权力。我们表明，尽管组合的实际值的复杂性，有一个有趣的递归公式（至少当有限域是素域），这很快导致许多有趣的结构事实，如黎曼假设Carlitz-戈斯zeta函数，单调性的程度，非零和特殊的身份分类功能字段multizeta，作为简单的后果。
We study the sum of integral powers of monic polynomials of a given degree over a finite field. The combinatorics of cancellations are quite complicated. We prove several results on the degrees of these sums giving direct or recursive formulas, congruence conditions and degree bounds for them. We point out a ‘duality’ between values for positive and negative powers. We show that despite the combinatorial complexity of the actual values, there is an interesting kind of a recursive formula (at least when the finite field is the prime field) which quickly leads to many interesting structural facts, such as Riemann hypothesis for Carlitz–Goss zeta function, monotonicity in degree, non-vanishing and special identity classification for function field multizeta, as easy consequences.