Lectures on P-Adic L-Functions

Kinkichi Iwasawa (Autor)

Buch | Softcover

112 Seiten

1972
Princeton University Press (Verlag)
978-0-691-08112-0 (ISBN)

Artikel merken

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.

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.

*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; chi), pg. 43* 6. AN ALTERNATE METHOD, pg. 66* 7. SOME APPLICATIONS, pg. 88*APPENDIX, pg. 100*BIBLIOGRAPHY, pg. 105

Erscheint lt. Verlag	21.7.1972
Reihe/Serie	Annals of Mathematics Studies
Verlagsort	New Jersey
Sprache	englisch
Maße	152 x 229 mm
Gewicht	170 g
Themenwelt	Mathematik / Informatik ► Mathematik
ISBN-10	0-691-08112-3 / 0691081123
ISBN-13	978-0-691-08112-0 / 9780691081120
Zustand	Neuware