1.

Record Nr.

UNINA9910450123003321

Autore

Itò„ Masami <1941->

Titolo

Algebraic theory of automata and languages [[electronic resource] /] / Masami Ito

Pubbl/distr/stampa

River Edge, N.J., : World Scientific, 2004

ISBN

1-281-87255-5

9786611872557

981-256-268-0

Descrizione fisica

1 online resource (210 p.)

Disciplina

511.3

Soggetti

Formal languages

Machine theory

Electronic books.

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Algebraic Theory of Automata and Languages; Preface; Contents; 0 Introduction; 1 Group-Matrix Type Automata; 2 General Automata; 3 Classes of Automata as Posets; 4 Languages and Operations; 5 Shuffle Closed Languages; 6 Insertions and Deletions; 7 Shuffles and Scattered Deletions; 8 Directable Automata; Bibliography; Index

Sommario/riassunto

Although there are some books dealing with algebraic theory ofautomata, their contents consist mainly of Krohn-Rhodes theory andrelated topics. The topics in the present book are ratherdifferent. For example, automorphism groups of automata and thepartially ordered sets of automata are systematicallydiscussed. Moreover, some operations on languages and special classesof regular languages associated with deterministic andnondeterministic directable automata are dealt with. The book isself-contained and hence does not require any knowledge of automataand formal languages.



2.

Record Nr.

UNINA9910790961403321

Autore

Yuan Xinyi <1981->

Titolo

The Gross-Zagier formula on Shimura curves [[electronic resource] /] / Xinyi Yuan, Shou-wu Zhang, and Wei Zhang

Pubbl/distr/stampa

Princeton, : Princeton University Press, 2012, c2013

ISBN

9786613883919

1-4008-4564-5

1-283-57146-3

Edizione

[Course Book]

Descrizione fisica

1 online resource (267 p.)

Collana

Annals of mathematics studies ; ; no. 184

Altri autori (Persone)

ZhangShouwu

ZhangWei <1981->

Disciplina

516.3/52

Soggetti

Shimura varieties

Arithmetical algebraic geometry

Automorphic forms

Quaternions

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Frontmatter -- Contents -- Preface -- Chapter One. Introduction and Statement of Main Results -- Chapter Two. Weil Representation and Waldspurger Formula -- Chapter Three. Mordell-Weil Groups and Generating Series -- Chapter Four. Trace of the Generating Series -- Chapter Five. Assumptions on the Schwartz Function -- Chapter Six. Derivative of the Analytic Kernel -- Chapter Seven. Decomposition of the Geometric Kernel -- Chapter Eight. Local Heights of CM Points -- Bibliography -- Index

Sommario/riassunto

This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations with rational coefficients attached naturally to abelian varieties parametrized by Shimura curves. This is followed by a complete proof of its coherent analogue: the



Waldspurger formula, which relates the periods of integrals and the special values of L-series by means of Weil representations. The Gross-Zagier formula is then reformulated in terms of incoherent Weil representations and Kudla's generating series. Using Arakelov theory and the modularity of Kudla's generating series, the proof of the Gross-Zagier formula is reduced to local formulas. The Gross-Zagier Formula on Shimura Curves will be of great use to students wishing to enter this area and to those already working in it.