Last edited by Meztimuro
Wednesday, August 12, 2020 | History

6 edition of Geometric Modular Forms and Elliptic Curves found in the catalog.

Geometric Modular Forms and Elliptic Curves

by Haruzo Hida

  • 200 Want to read
  • 28 Currently reading

Published by World Scientific Publishing Company .
Written in English

    Subjects:
  • Algebra,
  • Algebraic Geometry,
  • Number Theory,
  • Algebraic Number Theory,
  • Mathematics,
  • Science/Mathematics,
  • Curves, Elliptic,
  • Geometry - Algebraic,
  • Forms, Modular

  • The Physical Object
    FormatHardcover
    Number of Pages350
    ID Numbers
    Open LibraryOL9850858M
    ISBN 109810243375
    ISBN 109789810243371

    This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura-Taniyama conjecture, is : Professor Haruzo Hida. The two subjects--elliptic curves and modular forms--come together in Eichler-Shimura theory, which constructs elliptic curves out of modular forms of a special kind. The converse, that all rational elliptic curves arise this way, is called the Taniyama-Weil Conjecture and is .

    A modular elliptic curve is an elliptic curve E that admits a parametrisation X 0 (N) → E by a modular is not the same as a modular curve that happens to be an elliptic curve, something that could be called an elliptic modular curve. The modularity theorem, also known as the Taniyama–Shimura conjecture, asserts that every elliptic curve defined over the rational numbers is modular. Geometric Modular Forms and Elliptic Curves. Haruzo Hida Geometric Modular Forms and Elliptic Curves Haruzo Hida This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a.

    a modular curve of the form X 0(N). Any such elliptic curve has the property that its Hasse-Weil zeta function has an analytic continuation and satisfies a functional equation of the standard type. If an elliptic curve over Qwith a given j-invariant is modular then it is easy to see that all elliptic curves withCited by: A super great chapter on modular forms: Chapter 1-Elliptic modular forms and their applications- by Zagier in `The of Modular forms'. It can be read in an .


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Geometric Modular Forms and Elliptic Curves by Haruzo Hida Download PDF EPUB FB2

This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura-Taniyama conjecture, is by: This book should obviously be carefully studied by advanced students and by professional mathematicians in arithmetic algebraic geometry or (modern) number theory." -- Mathematical Reviews "Geometric Modular Forms and Elliptic Curves is suited for both the (advanced and specialized) classroom and (well-prepared and highly motivated) reader bent Format: Hardcover.

“Geometric Modular Forms and Elliptic Curves is suited for both the (advanced and specialized) classroom and (well-prepared and highly motivated) reader bent of serious self-study.

Beyond this, the book's prose is clear, there are examples and exercises available, and, as always, the serious student should have a go at them: he will reap. Get this from a library. Geometric modular forms and elliptic curves.

[Haruzo Hida] -- This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms.

The construction of Galois representations. This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof Price: $ This book concentrates on motivating the definitions, explaining the statements of the theorems and conjectures, making connections, and providing lots of examples, rather than dwelling on the hard proofs.

The book succeeds if, after reading the text, students feel compelled to study elliptic curves and modular forms in all their glory. Geometric Modular Forms and Elliptic Curves Haruzo Hida. This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms.

The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura - Taniyama conjecture, is given.

Geometric Modular Forms of Level 1; Elliptic Curves over ℂ; Elliptic Curves over p–Adic Fields; Level Structures; L–Functions of Elliptic Curves; Regularity; p–Ordinary Moduli Problems; Deformation of Elliptic Curves; Geometric Modular Forms: Integrality; Vertical Control Theorem; Action of GL(2) on Modular Forms; Jacobians and Galois.

Geometric modular forms and elliptic curves. [Haruzo Hida] elliptic curves; geometric modular forms; Jacobians and Galois representations; modularity problems.

The book's prose is clear, there are examples and exercises available, and, as always, the serious student should have a go at them: he will reap wonderful benefits.

This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura -- Taniyama conjecture, is given.

In addition, the book presents an outline of the proof of diverse modularity results of two-dimensional. Having been tested at UCLA and Hokkaido, Geometric Modular Forms and Elliptic Curves is suited for both the (advanced and specialized) classroom and (well-prepared and highly motivated) reader bent of serious self-study.

There is really a non-negotiable set of prerequisites hiding in the shadows: a good deal of number theory is needed, as well.

Geometric Modular Forms and Elliptic Curves Haruzo Hida. This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura-Taniyama conjecture, is given.

Elliptic Curves And Modular Forms by Robert C. Rhoades File Type: PDF Number of Pages: Description This note is an introduction to elliptic curves and modular forms.

These play a central role in modern arithmetical geometry and even in applications to cryptography. In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth theory of modular forms therefore belongs to complex analysis but the main importance of the theory has traditionally been in its connections with number theory.

Free Online Library: Geometric modular forms and elliptic curves, 2d ed.(Brief article, Book review) by "Reference & Research Book News"; Publishing industry Library and information science Books Book reviews.

This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura - Taniyama conjecture, is : Hida, Haruzo.

This textbook covers the basic properties of elliptic curves and modular forms, with emphasis on certain connections with number theory. The ancient "congruent number problem" is the central motivating example for most of the book. My purpose is to make the subject accessible to those who find it.

This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura-Taniyama conjecture, is given.

Introduction The thesis has the aim to study the Eichler-Shimura construction associating elliptic curves to weight-2 modular forms for Γ 0(N): this is the perfect topic to combine and develop further results from three courses I took in the first.

Introduction to Elliptic Curves and Modular Forms: Edition 2 - Ebook written by Neal I. Koblitz. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Introduction to Elliptic Curves and Modular Forms: Edition 2.

The theory of elliptic curves and modular forms is one subject where the most diverse branches of Mathematics like complex analysis, algebraic geometry, representation theory and number theory come together. Our point of view will be number theoretic. A well-known feature of number theory is theFile Size: KB.Elliptic Curves, Modular Forms and Cryptography Proceedings of the Advanced Instructional Workshop on Algebraic Number Theory.

Search within book. Front Matter. Pages i-viii. PDF. Elliptic Curves. Front Matter. Pages PDF. An overview. Elliptic Curves and Cryptography. R. Balasubramanian. Pages About this book.Elliptic curves over general rings 20 Geometric modular forms 22 Topological Fundamental Groups 23 Classical Weierstrass Theory 25 Complex Modular Forms 26 Hurwitz’s theorem, an application 28 4.

Elliptic curves over p–adic fields 30 Power series identities 30 Tate curves 33 References 36 In this.