黎曼ζ函数的有效通用性定理

IF 1.1 3区数学 Q1 MATHEMATICS

Commentarii Mathematici Helvetici Pub Date : 2016-11-30 DOI:10.4171/CMH/448

Youness Lamzouri, S. Lester, Maksym Radziwill

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引用次数: 12

摘要

当T足够大时，设0。这是由Bagchi改进的，他证明了这种t∈[0,t]的测度是(c(e)+o(1)) t，对于除最多可数个数之外的所有e b> 0。使用一种完全不同的方法，我们得到了Voronin定理的第一个有效版本，通过证明在收敛速度上可以节省t的对数的一个小幂次。我们的方法是灵活的，并且可以推广到其他l -函数在t方面，以及在导体方面的l -函数族。

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An effective universality theorem for the Riemann zeta function

Let 0 0, once T is large enough. This was refined by Bagchi who showed that the measure of such t∈[0,T] is (c(e)+o(1))T, for all but at most countably many e>0. Using a completely different approach, we obtain the first effective version of Voronin's Theorem, by showing that in the rate of convergence one can save a small power of the logarithm of T. Our method is flexible, and can be generalized to other L-functions in the t-aspect, as well as to families of L-functions in the conductor aspect.

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来源期刊

Commentarii Mathematici Helvetici 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Commentarii Mathematici Helvetici (CMH) was established on the occasion of a meeting of the Swiss Mathematical Society in May 1928. The first volume was published in 1929. The journal soon gained international reputation and is one of the world''s leading mathematical periodicals. Commentarii Mathematici Helvetici is covered in: Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.