期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2003
卷号：100
期号：12
页码：6904-6909
DOI：10.1073/pnas.1131697100
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Although there is vast literature on the values of L functions at nonpositive integers, the recent appearance of some of these values as the coefficients of specializations of knot invariants comes as a surprise. Using work of G. E. Andrews [(1981) Adv. Math. 41, 173-185; (1986) q-Series: Their Development and Application in Analysis, Combinatories, Physics, and Computer Algebra, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics 66 (Am. Math. Soc, Providence, RI); (1975) Problems and Prospects for Basic Hypergeometric Series: The Theory and Application of Special Functions (Academic, New York); and (1992) Illinois J. Math. 36, 251-274], we revisit this old subject and provide uniform and general results giving such generating functions as specializations of basic hypergeometric functions. For example, we obtain such generating functions for all nontrivial Dirichlet L functions.
