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Monday, July 27, 2020 | History

4 edition of Abelian varieties theta functions and the Fourier transforms found in the catalog.

Abelian varieties theta functions and the Fourier transforms

by Alexander Polishchuk

  • 168 Want to read
  • 5 Currently reading

Published by Cambridge University Press in Cambridge, UK, New York .
Written in

    Subjects:
  • Abelian varieties.,
  • Fourier transformations.

  • Edition Notes

    Includes bibliographical references (p. 283-289) and index.

    StatementAlexander Polishchuk.
    SeriesCambridge tracts in mathematics -- 153
    Classifications
    LC ClassificationsQA564 .P64 2003
    The Physical Object
    Paginationxvi, 292 p. :
    Number of Pages292
    ID Numbers
    Open LibraryOL22498577M
    ISBN 100521808049

    As an example, fast quantum Fourier transforms for all 4 classes of non-abelian 2-groups with cyclic normal subgroup of index 2 are explicitly constructed in terms of quantum circuits. The (quantum) complexity of the Fourier transform for these groups of size 2^n is O(n^2) in all cases. Title: Heisenberg Groups and the Fourier Transform Abstract: I will discuss the relationship between Fourier transforms and the Heisenberg groups, with a view toward the discussion of line bundles on complex tori that appears in Polishchuk's book Abelian Varieties, Theta functions, and .

    On Fourier Transforms and Delta Functions The Fourier transform of a function (for example, a function of time or space) provides a way to analyse the function in terms of its sinusoidal components of different wavelengths. The function itself is a sum of such components. That is, we present several functions and there corresponding Fourier Transforms. The derivation can be found by selecting the image or the text below. For convenience, we use both common definitions of the Fourier Transform, using the (standard for this website) variable f, .

    Robert Clifford Gunning 3 Rieman surfaces and generalized theta functions, Springer-Verlag, Berlin and New York, , pages. Complex numbers and complex variables, McGraw-Hill Yearbook of Science and Technol-ogy (), On the divisor order of vector bundles of rank two on a Riemann surface, Bulletin Inst. Math. LECTURE THE FOURIER ANALYSIS ON FINITE ABELIAN GROUPS 3 condition and the homomorphism condition, as stated in the special case of Z/NZ. The last one is embedded in the definition of characters, and now we consider the.


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Abelian varieties theta functions and the Fourier transforms by Alexander Polishchuk Download PDF EPUB FB2

ABELIAN VARIETIES, THETA FUNCTIONS AND - Abelian Varieties, Theta Functions and the Fourier Transform Alexander Polishchuk Frontmatter More information. CAMBRIDGETRACTSINMATHEMATICS is a categorification of the space of. Abelian Varieties, Theta Functions and the Fourier Transform (Cambridge Tracts in Mathematics Book ) - Kindle edition by Alexander Polishchuk.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Abelian Varieties, Theta Functions and the Fourier Transform (Cambridge Tracts in Mathematics Book ).Reviews: 1.

The aim of this book is to present a modern treatment of the theory of theta functions in the context of algebraic geometry.

The novelty of its approach lies in the systematic use of the Fourier-Mukai thebindyagency.com by: A catalog record for this book is available from the British Library. Library of Congress Cataloging in Publication Data Polishchuk, Alexander, – Abelian varieties, Theta functions and the Fourier transform / Alexander Polishchuk.

– (Cambridge tracts in mathematics ; ) Includes bibliographical references and index. ISBN Find helpful customer reviews and review ratings for Abelian Varieties, Theta Functions and the Fourier Transform (Cambridge Tracts in Mathematics Book ) at thebindyagency.com Read honest and unbiased product reviews from our users.4/5(1).

In his book Abelian Varieties, David Mumford defines an abelian variety over an algebraically closed field k k to be a complete algebraic group over k k.

Remarkably, any such thing is an abelian algebraic group. The assumption of connectedness is necessary for that conclusion. Automatic abelianness. Baker, Abelian Functions: Abel's Theorem and the Allied Theory of Theta Functions; Twentieth century.

c The theory of Poincaré normal functions implies that the Picard variety and Albanese variety are isogenous. Torelli's theorem; Gaetano. There is a close connection between the definition of Fourier series and the Fourier transform for functions f that are zero outside an interval.

For such a function, we can calculate its Fourier series on any interval that includes the points where f is not identically zero. The Fourier transform is also defined for such a function. 图书Abelian Varieties, Theta Functions and the Fourier Transform 介绍、书评、论坛及推荐.

The aim of this book is to present a modern treatment of the theory of theta functions in the context of algebraic geometry.

The novelty of its approach lies in the systematic use of the Fourier-Mukai transform. Abelian Varieties Author: Alexander Polishchuk.

Programme: Using Polishchuk's book [1] Abelian Varieties, Theta Functions and the Fourier transform we want to understand the modern technique of Fourier-Mukai thebindyagency.com a concrete goal we aim for Beilinson's and Polishchuk's [2] proof of the Torelli theorem which uses Fourier-Mukai transforms.

Heuristic behind the Fourier-Mukai transform. Ask Question Asked 10 years, I think Huybrechts' book "Fourier-Mukai transforms in algebraic geometry" is a good book to look at. Abelian Varieties, Theta Functions and the Fourier Transform, Cambridge Tracts in MathematicsCambridge University Press, This also happens to be one.

This book explores the theory of abelian varieties over the field of complex numbers, explaining both classic and recent results in modern language. The second edition adds five chapters on recent results including automorphisms and vector bundles on abelian varieties, algebraic cycles and the Hodge conjecture.

" far more readable than most it is also much more complete.". THE FOURIER TRANSFORM FOR LOCALLY COMPACT ABELIAN GROUPS DAN SU Abstract. An introduction to locally compact abelian algebraic groups and the usage of dual groups and Fourier transforms to study them.

Contents 1. Introduction 1 2. Preliminaries on Topological Groups 2 3. Characters and the Dual Group 3 4. Structure Spaces and The Gelfand. COHERENT STATE TRANSFORMS AND ABELIAN VARIETIES 5 functions ˜θ are holomorphic sections of Lk, θ˜ ∈ H0(M,Lk).Using the automorphy factors (8), we see that the space H0(M,Lk) is naturally iso- morphic with the space of holomorphic functions θ on V such that.

Quantization of abelian varieties: Distributional sections and the transition from Kähler to real polarizations Article in Journal of Functional Analysis (10) · July with 35 Reads. The purpose of this paper is to give two applications of Fourier transforms and generic vanishing theorems: we give a cohomological characterization of.

The finite Fourier-transform is considered as a linear transformation on a certain space of theta functions and thereby is seen to induce an invertible morphism of Abelian varieties. This is explained in the context of the representation theory of the finite symplectic thebindyagency.com by: 3.

Nov 15,  · Let G be a finite nonabelian group. Bent functions on G are defined by the Fourier transforms at irreducible representations of G. We introduce a dual basis $${\widehat{G}}$$, consisting of functions on G determined by its unitary irreducible representations, that will play a role similar to the dual group of a finite abelian thebindyagency.com by: 2.

Transformations Books Browse New & Used Transformations Books. Results 1 - 50 of for Transformations Books. Fourier Transforms by Sneddon, Ian N. ISBN: List Price: $ $ (Save 37%) 2. Abelian Varieties and the Fourier Mukai The positive definiteness of H implies the convergence of the theta series.

They provide enough sections of L for an embedding of X into a projective space. Let C be a compact Riemann surface of genus g. We consider the space V:. $\begingroup$ Theta functions naturally arise in many areas, such as number theory (including the theories of abelian varieties and moduli spaces, and of quadratic forms), combinatorics, physics etc.

- see here for references. $\endgroup$ – Dietrich Burde May 30 '14 at Abelian Chern-Simons theory relates classical theta functions to the topological quantum field theory of the linking number of knots. In this paper we explain how to derive the constructs of.There are Fourier expansions on nite abelian groups essentially identical in form to Fourier expansions of periodic functions on the real line.

1. Fourier analysis on nite abelian groups The main consequence for Fourer expansions can be stated without mentioning many of the key ideas of the proofs.

Let Gbe a nite abelian group, and L2(G) the.