Lectures on P-Adic L-Functions (eBook)

Kinkichi Iwasawa (Autor)

eBook Download: PDF

2016
112 Seiten
Princeton University Press (Verlag)
978-1-4008-8170-3 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 2.3.2016
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• Schlagworte: Abelian extension • absolute value • Algebraically closed field • algebraic closure • algebraic number • algebraic number field • algebraic number theory • Arithmetic function • class field theory • complex number • conjecture • Cyclotomic field • Dirichlet character • existential quantification • finite group • Integer • L-Function • mellin transform • Meromorphic Function • Multiplicative group • P-adic L-function • P-adic number • power series • Prime number • Quadratic field • Rational number • real number • Root of unity • scientific notation • Series (mathematics) • Special case • SUBGROUP • Theorem • Topology
• ISBN-10: 1-4008-8170-6 / 1400881706
• ISBN-13: 978-1-4008-8170-3 / 9781400881703