Number Theory

Lectures on p-adic L-functions by Kinkichi Iwasawa

Posted On March 23, 2017 at 12:28 pm by / Comments Off on Lectures on p-adic L-functions by Kinkichi Iwasawa

By Kinkichi Iwasawa

Those are notes of lectures given at Princeton college in the course of the fall semester of 1969. The notes current an advent to p-adic L-functions originated in Kubota-Leopoldt {10} as p-adic analogues of classical L-functions of Dirichlet.

Show description

Read Online or Download Lectures on p-adic L-functions PDF

Similar number theory books

Topological Vector Spaces

In the event you significant in mathematical economics, you return throughout this ebook time and again. This booklet comprises topological vector areas and in the community convex areas. Mathematical economists need to grasp those subject matters. This booklet will be a very good aid for not just mathematicians yet economists. Proofs aren't difficult to persist with

Game, Set, and Math: Enigmas and Conundrums

A set of Ian Stewart's leisure columns from Pour los angeles technological know-how, which show his skill to deliver sleek maths to existence.

Proceedings of a Conference on Local Fields: NUFFIC Summer School held at Driebergen (The Netherlands) in 1966

From July 25-August 6, 1966 a summer season institution on neighborhood Fields used to be held in Driebergen (the Netherlands), prepared through the Netherlands Universities origin for foreign Cooperation (NUFFIC) with monetary help from NATO. The clinical organizing Committl! e consisted ofF. VANDER BLIJ, A. H. M.

Multiplicative Number Theory

The hot version of this thorough exam of the distribution of top numbers in mathematics progressions deals many revisions and corrections in addition to a brand new part recounting contemporary works within the box. The e-book covers many classical effects, together with the Dirichlet theorem at the life of top numbers in arithmetical progressions and the theory of Siegel.

Extra resources for Lectures on p-adic L-functions

Sample text

Hence The function L p (s; X) is uniquely characterized also by i) and by the above equalities. §3. l) -1, =0 If n '" 0 mod e, then n is even so that Bn, X � 0 by Theorem 2, §2. Hence, by the uniqueness mentioned above, if XC-I) = -1. On the other hand, if XC-I) 1, then for n == 0 mod e so that for n;:: 1, n == 0 mod e. Hence Lp Cs; X) is certainly not identically O. 5. converse of Theorem 1 is also partially true. Although this will never be used in the following (exce pt for an elementary lemma below), the result seems inter� esting enough to be mentioned here.

Ai d�i ) . i=o If A(x) beloogs to Q K ' it follows from Lemma 5, §3 that xaxCl ai d�) I) S �a 1> - 0 - 0 Therefore, for each n ? 0, defines a linear map with LEMMA 3. For A E QK ' s f Zp , where the limit is taken over any sequence of integers ni' i that n i � 0, p-1 1 ni' and such that as i � "" . ::: 0, such 50 p-ADlC L-FUNCTIONS (Since the integers n �0 with p-1 1 n are everywhere dense in Zp ' such a sequence always exists for any given s in Zp ' ) Proof.

We have to sh ow that ! Yn(s)! ::: l n f ! for all s integer, m � 0, such that p-1 I m , Then n yn(m) "" 2: i=o n = (_1)n -i (i) ¢(i, m) I (-1 l-i (n im i=o pri < Z ' Let m be an p Zp 46 p -ADIC L-FUNCTIONS because ¢(i, m) = m = ·m 1 fo r p Y i , p-1 1 m , and p fo. 2. It follows that n yn(m) '" l (_l)n -i i= o (�) im The sum on the right is the integer d�) introduced in 3 . 5 and we know (Lemma 5, §3) that it is divisible by n L Hence we have Now, the integers m such as mention ed above are everywhere dense in Zp ' Therefore lyn (s)1 s: In!

Download PDF sample

Rated 4.25 of 5 – based on 50 votes