Borcherds Products On O 2 L And Chern Classes Of Heegner Divisors

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Borcherds Products On O 2 L And Chern Classes Of Heegner Divisors

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Author : Jan H. Bruinier
language : en
Publisher: Springer
Release Date : 2004-10-11

Borcherds Products On O 2 L And Chern Classes Of Heegner Divisors written by Jan H. Bruinier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-11 with Mathematics categories.

Around 1994 R. Borcherds discovered a new type of meromorphic modular form on the orthogonal group $O(2,n)$. These "Borcherds products" have infinite product expansions analogous to the Dedekind eta-function. They arise as multiplicative liftings of elliptic modular forms on $(SL)_2(R)$. The fact that the zeros and poles of Borcherds products are explicitly given in terms of Heegner divisors makes them interesting for geometric and arithmetic applications. In the present text the Borcherds' construction is extended to Maass wave forms and is used to study the Chern classes of Heegner divisors. A converse theorem for the lifting is proved.

Borcherds Products On O 2 L And Chern Classes Of Heegner Divisors

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Author : Jan Hendrik Bruinier
language : en
Publisher:
Release Date : 2000

Borcherds Products On O 2 L And Chern Classes Of Heegner Divisors written by Jan Hendrik Bruinier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.

Geometry And Analysis Of Automorphic Forms Of Several Variables

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Author : Yoshinori Hamahata
language : en
Publisher: World Scientific
Release Date : 2012

Geometry And Analysis Of Automorphic Forms Of Several Variables written by Yoshinori Hamahata and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

This volume contains contributions of principal speakers of the symposium on geometry and analysis of automorphic forms of several variables, held in September 2009 at Tokyo, Japan, in honor of Takayuki Oda''s 60th birthday. It presents both research and survey articles in the fields that are the main themes of his work. The volume may serve as a guide to developing areas as well as a resource for researchers who seek a broader view and for students who are beginning to explore automorphic form.

Enumerative Invariants In Algebraic Geometry And String Theory

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Author : Marcos Marino
language : en
Publisher: Springer
Release Date : 2008-08-15

Enumerative Invariants In Algebraic Geometry And String Theory written by Marcos Marino and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-15 with Mathematics categories.

Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as that of Gromov-Witten invariants) leading in turn to the solution of problems in enumerative geometry. Conversely, the availability of mathematically rigorous definitions and theorems has benefited the physics research by providing the required evidence in fields where experimental testing seems problematic. The aim of this volume, a result of the CIME Summer School held in Cetraro, Italy, in 2005, is to cover part of the most recent and interesting findings in this subject.

L Functions And Automorphic Forms

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Author : Jan Hendrik Bruinier
language : en
Publisher: Springer
Release Date : 2018-02-22

L Functions And Automorphic Forms written by Jan Hendrik Bruinier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-22 with Mathematics categories.

This book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "Automorphic Forms and L-Functions", held at the University of Heidelberg in 2016. The theory of automorphic forms and their associated L-functions is one of the central research areas in modern number theory, linking number theory, arithmetic geometry, representation theory, and complex analysis in many profound ways. The 19 papers cover a wide range of topics within the scope of the conference, including automorphic L-functions and their special values, p-adic modular forms, Eisenstein series, Borcherds products, automorphic periods, and many more.

Information Geometry

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Author : Khadiga Arwini
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-25

Information Geometry written by Khadiga Arwini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-25 with Computers categories.

This volume will be useful to practising scientists and students working in the application of statistical models to real materials or to processes with perturbations of a Poisson process, a uniform process, or a state of independence for a bivariate process. We use information geometry to provide a common differential geometric framework for a wide range of illustrative applications including amino acid sequence spacings in protein chains, cryptology studies, clustering of communications and galaxies, cosmological voids, coupled spatial statistics in stochastic fibre networks and stochastic porous media, quantum chaology. Introduction sections are provided to mathematical statistics, differential geometry and the information geometry of spaces of probability density functions.

Alternative Pseudodifferential Analysis

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Author : André Unterberger
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-03

Alternative Pseudodifferential Analysis written by André Unterberger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-03 with Mathematics categories.

This volume introduces an entirely new pseudodifferential analysis on the line, the opposition of which to the usual (Weyl-type) analysis can be said to reflect that, in representation theory, between the representations from the discrete and from the (full, non-unitary) series, or that between modular forms of the holomorphic and substitute for the usual Moyal-type brackets. This pseudodifferential analysis relies on the one-dimensional case of the recently introduced anaplectic representation and analysis, a competitor of the metaplectic representation and usual analysis. Besides researchers and graduate students interested in pseudodifferential analysis and in modular forms, the book may also appeal to analysts and physicists, for its concepts making possible the transformation of creation-annihilation operators into automorphisms, simultaneously changing the usual scalar product into an indefinite but still non-degenerate one.

Optimal Transportation Networks

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Author : Marc Bernot
language : en
Publisher: Springer Science & Business Media
Release Date : 2009

Optimal Transportation Networks written by Marc Bernot and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Business & Economics categories.

The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees. These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume.

Compactifying Moduli Spaces For Abelian Varieties

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Author : Martin C. Olsson
language : en
Publisher: Springer
Release Date : 2008-07-25

Compactifying Moduli Spaces For Abelian Varieties written by Martin C. Olsson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-25 with Mathematics categories.

This volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa.

The Principle Of Least Action In Geometry And Dynamics

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Author : Karl Friedrich Siburg
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-05-17

The Principle Of Least Action In Geometry And Dynamics written by Karl Friedrich Siburg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-17 with Computers categories.

New variational methods by Aubry, Mather, and Mane, discovered in the last twenty years, gave deep insight into the dynamics of convex Lagrangian systems. This book shows how this Principle of Least Action appears in a variety of settings (billiards, length spectrum, Hofer geometry, modern symplectic geometry). Thus, topics from modern dynamical systems and modern symplectic geometry are linked in a new and sometimes surprising way. The central object is Mather’s minimal action functional. The level is for graduate students onwards, but also for researchers in any of the subjects touched in the book.