# Read e-book online A First Course in Modular Forms (Graduate Texts in PDF

By Fred Diamond,Jerry Shurman

ISBN-10: 038723229X

ISBN-13: 9780387232294

ISBN-10: 1441920056

ISBN-13: 9781441920058

This ebook introduces the idea of modular varieties, from which all rational elliptic curves come up, with a watch towards the Modularity Theorem. dialogue covers elliptic curves as advanced tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner thought; Hecke eigenforms and their mathematics homes; the Jacobians of modular curves and the Abelian types linked to Hecke eigenforms. because it offers those principles, the ebook states the Modularity Theorem in a number of kinds, referring to them to one another and referring to their purposes to quantity idea. The authors suppose no historical past in algebraic quantity conception and algebraic geometry. workouts are included.

**Read or Download A First Course in Modular Forms (Graduate Texts in Mathematics) PDF**

**Best number theory books**

This publication grew out of a path which I gave in the course of the iciness time period 1997/98 on the Universitat Munster. The path lined the fabric which this is offered within the first 3 chapters. The fourth extra complex bankruptcy used to be further to offer the reader a slightly entire travel via the entire very important features of the idea of in the neighborhood convex vector areas over nonarchimedean fields.

**Automorphic Forms and L-Functions for the Group GL(n,R) by Dorian Goldfeld PDF**

L-functions linked to automorphic kinds encode all classical quantity theoretic details. they're corresponding to hassle-free debris in physics. This 2006 e-book offers a completely self-contained advent to the idea of L-functions in a method available to graduate scholars with a simple wisdom of classical research, complicated variable conception, and algebra.

**The Arithmetic of Elliptic Curves: 106 (Graduate Texts in by Joseph H. Silverman PDF**

The idea of elliptic curves is distinct through its lengthy heritage and by way of the range of the tools which were utilized in its examine. This e-book treats the mathematics procedure in its sleek formula, by utilizing uncomplicated algebraic quantity idea and algebraic geometry. Following a short dialogue of the required algebro-geometric effects, the ebook proceeds with an exposition of the geometry and the formal staff of elliptic curves, elliptic curves over finite fields, the complicated numbers, neighborhood fields, and international fields.

The ebook bargains with the (elementary and introductory) idea of valuation jewelry. As defined within the creation, this represents an invaluable and significant standpoint in algebraic geometry, specifically in regards to the thought of algebraic curves and their functionality fields. The correspondences of this with different viewpoints (e.

- Multiple Zeta Functions, Multiple Polylogarithms and Their Special Values: 12 (Series on Number Theory and Its Applications)
- Geodesic and Horocyclic Trajectories (Universitext)
- Elliptic Cohomology (University Series in Mathematics)
- Discourses on Algebra (Universitext)
- Algorithmic Algebraic Number Theory (Encyclopedia of Mathematics and its Applications)
- Elements of Logic via Numbers and Sets (Springer Undergraduate Mathematics Series)

**Extra info for A First Course in Modular Forms (Graduate Texts in Mathematics)**

**Example text**

### A First Course in Modular Forms (Graduate Texts in Mathematics) by Fred Diamond,Jerry Shurman

by Jason

4.5