β Scribed by Kinkichi Iwasawa
No coin nor oath required. For personal study only.
An especially timely work, the book is an introduction to the theory of p-adic L-functions originated by Kubota and Leopoldt in 1964 as p-adic analogues of the classical L-functions of Dirichlet.
Professor Iwasawa reviews the classical results on Dirichlet's L-functions and sketches a proof for some of them. Next he defines generalized Bernoulli numbers and discusses some of their fundamental properties. Continuing, he defines p-adic L-functions, proves their existence and uniqueness, and treats p-adic logarithms and p-adic regulators. He proves a formula of Leopoldt for the values of p-adic L-functions at s=1. The formula was announced in 1964, but a proof has never before been published. Finally, he discusses some applications, especially the strong relationship with cyclotomic fields.
CONTENTS
PREFACE
Β§1. Dirichletβs L-functions
Β§2. Generalized Bernoulli Numbers
Β§3. p-Adic L-functions
Β§4. p-Adic Logarithms and p-Adic Regulators
Β§5. Calculation of Lp(1; Ο)
Β§6. An Alternate Method
Β§7. Some Applications
APPENDIX
BIBLIOGRAPHY
π SIMILAR VOLUMES
These are notes of lectures given at Princeton University during the fall semester of 1969. The notes present an introduction to p-adic L-functions originated in Kubota-Leopoldt {10} as p-adic analogues of classical L-functions of Dirichlet.
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