Hypergeometric generating functions for values of Dirichlet and other L functions
AUTOR(ES)
Lovejoy, Jeremy
FONTE
National Academy of Sciences
RESUMO
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.
ACESSO AO ARTIGO
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=165802Documentos Relacionados
- Classification of hypergeometric identities for π and other logarithms of algebraic numbers
- ON GENERATING FUNCTIONS FOR RESTRICTED PARTITIONS OF RATIONAL INTEGERS
- ON GENERATING FUNCTIONS FOR RESTRICTED PARTITIONS OF RATIONAL INTEGERS
- PROBABILITY GENERATING FUNCTIONS AND THEIR ITERATES*
- SOME BILINEAR GENERATING FUNCTIONS*