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Thursday, July 30, 2020 | History

3 edition of Galois theory and modular forms found in the catalog.

Galois theory and modular forms

# Galois theory and modular forms

Written in English

Edition Notes

Classifications The Physical Object Statement edited by Ki-ichiro Hashimoto, Katsuya Miyake, Hiroaki Nakamura. LC Classifications QA76 Pagination xi, 393 p. : Number of Pages 393 Open Library OL22562638M ISBN 10 1402076894

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): In this course, assuming basic knowledge of algebraic number theory, commutative algebra and topology, we study non-archimedean deformation theory of modular forms on GL(2) and modular Galois representations into GL(2). We plan to discuss the following four topics: (1) analytic/algebraic theory of elliptic modular. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes.

Abstract: This is a book about computational aspects of modular forms and the Galois representations attached to them. The main result is the following: Galois representations over finite fields attached to modular forms of level one can, in almost all cases, be computed in polynomial time in the weight and the size of the finite field. In mathematics, a Galois module is a G-module, with G being the Galois group of some extension of term Galois representation is frequently used when the G-module is a vector space over a field or a free module over a ring in representation theory, but can also be used as a synonym for study of Galois modules for extensions of local or global fields is an important tool.

GALOIS REPRESENTATIONS AND MOD ULAR FORMS 3 acting as z7! az+b cz+d The invariance of f(z)dz means that f(z)dz arises by pullback from a di erential on the quotient Y 0(N):=Γ 0(N) quotient is a non-compact Riemann sur-face with a standard compacti cation known as X 0(N).The complement of Y 0(N) in X 0(N) is a nite set, the set of cusps of X 0(N).The conditions on in nity. This is a book about computational aspects of modular forms and the Galois representations attached to them. The main result is the following: Galois representations over finite fields attached to.

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In September,an international conference "Galois Theory and Modular Forms" was held at Tokyo Metropolitan University after some preparatory work­ shops and symposia in previous years. The title of this book came from that of the conference, and the authors were participants of those meet­ All of the articles here were critically.

ISBN: OCLC Number: Description: xi, pages: illustrations ; 25 cm. Contents: The arithmetic of Weierstrass points on modular curves X[subscript 0](p) / Scott Ahlgren --Semistable abelian varieties with small division fields / Armand Brumer and Kenneth Kramer --Q-curves with rational j-invariants and jacobian surfaces of GL[subscript 2]-type / Ki-ichiro.

Get this from a library. Galois theory and modular forms. [K Hashimoto; Katsuya Miyake; Hiroaki Nakamura;] -- The key words for the book are "Galois groups", or more precisely "generic polynomials", "Galois coverings of algebraic curves" and "Shimura varieties".

The. Buy Galois Theory and Modular Forms (Developments in Mathematics) on FREE SHIPPING on qualified orders Galois Theory and Modular Forms (Developments in Mathematics): Ki-ichiro Hashimoto: : BooksCited by: 8. $\begingroup$ You can try Diamond and Shurman's book "A First Course in Modular Forms".

Galois rep-s are covered in the last chapter. Galois rep-s are covered in the last chapter. If you find it hard, you can try Goldfeld and Hundley's "Automorphic Representations and L-Functions for the General Linear Group".

Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan’s tau-function as a typical example, have deep arithmetic significance.

The notes by Mladen Dimitrov present the basics of the arithmetic theory of Hilbert modular forms and varieties, with an emphasis on the study of the images of the attached Galois representations, on modularity lifting theorems over totally real number fields, and on the cohomology of Hilbert modular varieties with integral coefficients.

In September,an international conference "Galois Theory and Modular Forms" was held at Tokyo Metropolitan University after some preparatory work­ shops and symposia in previous years.

The title of this book came from that of the conference, and the authors were participants of those meet­ All of the articles here were critically Format: Hardcover. Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices.

Their Fourier coefficients, with Ramanujan's tau-function as a typical example, - Selection from Computational Aspects of Modular Forms and Galois Representations [Book].

Galois theory allows one to reduce certain problems in field theory, especially those related to field extensions, to problems in group theory.

(field-theory) tag instead. For questions about abstractions of Galois theory, use (galois-connections). galois-theory elliptic-curves modular-forms. asked May 6 at rogerl. k 3 3 gold. This is a book about computational aspects of modular forms and the Galois representations attached to them.

The main result is the following: Galois representations over ﬁnite ﬁelds attached to modular forms of level one can, in almost all cases, be computed in. Modular Functions and Modular Forms. pdf current version () Abstract This is an introduction to the arithmetic theory of modular functions and modular forms.

ical forms for matrices. These topics are covered in a standard graduate-level algebra course. I develop the properties of algebraic integers, valuation theory and completions within the text since they usually fall outside such a course.

Many people have read sections of File Size: 1MB. MODULAR FORMS AND THEIR GALOIS REPRESENTATIONS 2 number theory, DP/(p) is isomorphic to Gal(Qp/Qp) for the p-adic ﬁeld Qp and its alge- braic closure σ∈DP induces an automorphism of Z/P which is an algebraic closure Fp of Fp, we have an exat sequence of compact groups 1 →IP/p →DP/p →Gal(Fp/Fp) →1.

for Fp = OF /p. Thus there is a unique generator Frobp of. This book provides a comprehensive account of a key, perhaps the most important, theory that forms the basis of Taylor-Wiles proof of Fermat’s last theorem.

Hida begins with an overview of the theory of automorphic forms on linear algebraic groups and then covers the basic theory and recent results on elliptic modular forms, including a.

The Paperback of the Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau Due to COVID, orders may be delayed.

Thank you for your : Bas Edixhoven. The two main topics of this book are Iwasawa theory and modular forms. The presentation of the theory of modular forms starts with several beautiful relations discovered by Ramanujan and leads to a discussion of several important ingredients, including the zeta-regularized products, Kronecker's limit formula, and the Selberg trace formula.

Read "Computational Aspects of Modular Forms and Galois Representations How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM)" by Robin de Jong available from Rakuten Kobo.

Modular forms are tremendously important in various areas of Brand: Princeton University Press. This book provides a comprehensive account of a key, perhaps the most important, theory that forms the basis of Taylor-Wiles proof of Fermat's last theorem.

Hida begins with an overview of the theory of automorphic forms on linear algebraic groups and then covers the basic theory and recent results on elliptic modular forms, including a substantial simplification of the Taylor-Wiles proof by.

$\begingroup$ Dear David: A hint of the interaction with rep'n theory is already seen in the fact that the classical upper half-plane is a coset space for the Lie group ${\rm{GL}}_2(\mathbf{R})$, and relation of C-R eqns with Casimir in Lie alg., but need a more adelic formulation to see how the Hecke theory comes out from the action of a group also.

(Toy version: adelic formulation of. In this chapter we explicitly compute mod-ℓ Galois representations attached to modular forms. To be precise, we look at cases with ℓ ≤ 23, and the modular forms considered will be cusp forms of level 1 and weight up to We present the result in terms of polynomials associated with .This book provides a comprehensive account of a key, perhaps the most important, theory that forms the basis of Taylor-Wiles proof of Fermat's last theorem.

Hida begins with an overview of the theory of automorphic forms on linear algebraic groups and then covers the basic theory and recent results on elliptic modular forms, including a Price: \$This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 thro at Boston University.

Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular.