Printfusion E-books

Number Theory

Get P-Adic L-Functions and P-Adic Representations PDF

By Bernadette Perrin-Riou

ISBN-10: 0821819461

ISBN-13: 9780821819463

Ordinarily, $p$-adic $L$-functions were created from advanced $L$-functions through precise values and Iwasawa concept. during this quantity, Perrin-Riou provides a concept of $p$-adic $L$-functions coming at once from $p$-adic Galois representations (or, extra mostly, from motives). This conception encompasses, specifically, a building of the module of $p$-adic $L$-functions through the mathematics conception and a conjectural definition of the $p$-adic $L$-function through its detailed values. because the unique ebook of this ebook in French (see ""Asterisque"" 229, 1995), the sphere has passed through major growth. those advances are famous during this English variation. additionally, a few minor advancements were made to the textual content.

Show description

Read or Download P-Adic L-Functions and P-Adic Representations PDF

Similar number theory books

Basiswissen Zahlentheorie: Eine Einfuhrung in Zahlen und - download pdf or read online

Kenntnisse uber den Aufbau des Zahlsystems und uber elementare zahlentheoretische Prinzipien gehoren zum unverzichtbaren Grundwissen in der Mathematik. Das vorliegende Buch spannt den Bogen vom Rechnen mit naturlichen Zahlen uber Teilbarkeitseigenschaften und Kongruenzbetrachtungen bis hin zu zahlentheoretischen Funktionen und Anwendungen wie der Kryptographie und Zahlencodierung.

Read e-book online Selected Chapters of Geometry, Analysis and Number Theory: PDF

This ebook specializes in a few vital classical components of Geometry, research and quantity concept. the fabric is split into ten chapters, together with new advances on triangle or tetrahedral inequalities; specific sequences and sequence of actual numbers; quite a few algebraic or analytic inequalities with functions; precise functions(as Euler gamma and beta services) and distinctive capability( because the logarithmic, identric, or Seiffert's mean); mathematics services and mathematics inequalities with connections to excellent numbers or similar fields; and lots of extra.

Additional info for P-Adic L-Functions and P-Adic Representations

Sample text

70. (a) First, prove that if k and l are two nonnegative integers, one has 1 lim n→∞ 0 n x k xl dx = 1 . (k + 1)(l + 1) Second, approximate f and g by polynomials. 24 1 Special Limits (b) Prove, by using the substitution n/x = y, that 1 n x f n 0 1 dx − 0 f (x)dx = n 1 0 f (t) ∞ n ∑ (k + t)2 − 1 dt k=n and calculate the limit of the last integral by using Lebesgue Convergence Theorem. 71. Follow the steps: Step 1. Prove that if n is an integer and k and m are two nonnegative integers, then n+1 n yk ({y})m dy = k ∑ p=0 k np .

Use that sin2 (nx) + cos2 (nx) = 1. 25. Observe that k a (n2 + kn + a)α n 2α 1 n 1 + n + n2 = 2β −1 · ∑ ∑ 2 β n k=1 n k=1 (n + kn + b) 1 + nk + nb2 α n β , and prove that if a, b, u ≥ 0 are real numbers and v > 0, one has k a 1 n 1 + n + n2 lim ∑ n→∞ n k=1 1 + k + b2 n n u v = 1 0 (1 + x)u−v dx. 26. Denote the value of the limit by Ln , use that fn (x) = exp( fn−1 (x) ln x), and apply Lagrange’s Mean Value Theorem to the exponential function to prove that Ln = −Ln−1 . 28. Use that 1/(i + j) = the order of summation.

However, n kα ∑ nβ n→∞ lim 1 n kα ∑ α n→∞ n k=1 n = · lim k=1 lim 1 n→∞ nβ −α −1 = 0. Case 3. α + 1 > β . )α , where the last inequality follows from √ the Arithmetic Mean–Geometric Mean Inequality. Using Stirling’s formula, n! ∼ 2π n(n/e)n , we get that limn→∞ xn = ∞, and the problem is solved. 16. The limit equals eα /p . Let (xn )n∈N be the sequence defined by n ∑ ln xn = 1+ k=1 α k p−1 . ,n ⎞ α k p−1 ≤ xn p p−1 k=1 n − k n ⎠∑ k ln 1 + n αp −k p−1 p−1 α k p−1 n p −k p−1 ⎞ α k p−1 . ,n ⎞ ⎛ ⎠=1 and p−1 lim ⎝ max n→∞ ⎞ k ln 1+ nαp −k p−1 ⎠ = 1.

Download PDF sample

P-Adic L-Functions and P-Adic Representations by Bernadette Perrin-Riou


by Anthony
4.4

Rated 4.42 of 5 – based on 20 votes