Polylogarithms and Riemann's zeta function

被引:28
|
作者
Lee, MH
机构
[1] Department of Physics and Astronomy, University of Georgia, Athens, GA
来源
PHYSICAL REVIEW E | 1997年 / 56卷 / 04期
关键词
D O I
10.1103/PhysRevE.56.3909
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
Riemann's zeta function has been important in statistical mechanics for many years, especially for the understanding of Bose-Einstein condensation. Polylogarithms can yield values of Riemann's zeta function in a special limit. Recently these polylogarithm functions have unified the statistical mechanics of ideal gases. Our particular concern is obtaining the values of Riemann's zeta function of negative order suggested by a physical application of polylogs. We find that there is an elementary way of obtaining them, which also provides an insight into the nature of the values of Riemann's zeta function. It relies on two properties of polylogs-the recurrence and duplication relations. The relevance of the limit process in the statistical thermodynamics is described.
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页码:3909 / 3912
页数:4
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