Non-commutative polynomial reciprocity formulae

Authors
Fukuhara, S Matsumoto, Y Yui, N
Citation
S. Fukuhara et al., Non-commutative polynomial reciprocity formulae, INT J MATH, 12(8), 2001, pp. 973-986
Citations number
10
Categorie Soggetti
Mathematics
Journal title
INTERNATIONAL JOURNAL OF MATHEMATICS
ISSN journal
0129167X → ACNP
Volume
12
Issue
8
Year of publication
2001
Pages
973 - 986
Database
ISI
SICI code
0129-167X(200111)12:8<973:NPRF>2.0.ZU;2-4
Abstract
We prove non-commutative reciprocity formulae for certain polynomials using Fox's free differential calculus. The abelianizations of these reciprocity formulae rediscover the polynomial reciprocity formulae of Carlitz and Ber ndt-Dieter. Further, many other reciprocity formulae related to Dedekind su ms are rederived from our polynomial reciprocity formulae; these include, f or instance, generalizations of the classical Eisenstein reciprocity formul a.