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Lectures on P-Adic L-Functions. (AM-74)
Kinkichi Iwasawa

Paperback | 1972 | $60.00 | £49.95 | ISBN: 9780691081120
112 pp. | 6 x 9
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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.

Table of Contents:

  • Frontmatter, pg. i
  • PREFACE, pg. v
  • CONTENTS, pg. vii
  • §1. DIRICHLET’S L-FUNCTIONS, pg. 1
  • §2. GENERALIZED BERNOULLI NUMBERS, pg. 7
  • §3. p-ADIC L-FUNCTIONS, pg. 17
  • §4. p-ADIC LOGARITHMS AND p-ADIC REGULATORS, pg. 36
  • §5. CALCULATION OF Lp (1; χ), pg. 43
  • §6. AN ALTERNATE METHOD, pg. 66
  • §7. SOME APPLICATIONS, pg. 88
  • APPENDIX, pg. 100
  • BIBLIOGRAPHY, pg. 105

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