Pham Huu Tiep – författare & böcker

Exponential Sums, Hypergeometric Sheaves, and Monodromy Groups

Häftad, Engelska, 2025

611 kr

Skickas inom 5-8 vardagar

An examination of some of the remarkable connections between group theory and arithmetic algebraic geometry over finite fieldsExponential sums have been of great interest ever since Gauss, and their importance in analytic number theory goes back a century to Kloosterman. Grothendieck’s creation of the machinery of l-adic cohomology led to the understanding that families of exponential sums give rise to local systems, while Deligne, who gave his general equidistribution theorem after proving the Riemann hypothesis part of the Weil conjectures, established the importance of the monodromy groups of these local systems. Deligne’s theorem shows that the monodromy group of the local system incarnating a given family of exponential sums determines key statistical properties of the family of exponential sums in question. Despite the apparent simplicity of this relation of monodromy groups to statistical properties, the actual determination of the monodromy group in any particular situation is highly nontrivial and leads to many interesting questions.This book is devoted to the determination of the monodromy groups attached to various explicit families of exponential sums, especially those attached to hypergeometric sheaves, arguably the simplest local systems on G_m, and to some simple (in the sense of simple to write down) one-parameter families of one-variable sums. These last families turn out to have surprising connections to hypergeometric sheaves. One of the main technical advances of this book is to bring to bear a group-theoretic condition (S+), which, when it applies, implies very strong structural constraints on the monodromy group, and to show that (S+) does indeed apply to the monodromy groups of most hypergeometric sheaves.

Exponential Sums, Hypergeometric Sheaves, and Monodromy Groups

AvNicholas M. Katz,Pham Huu Tiep

Inbunden, Engelska, 2025

1 337 kr

Skickas inom 5-8 vardagar

An examination of some of the remarkable connections between group theory and arithmetic algebraic geometry over finite fieldsExponential sums have been of great interest ever since Gauss, and their importance in analytic number theory goes back a century to Kloosterman. Grothendieck’s creation of the machinery of l-adic cohomology led to the understanding that families of exponential sums give rise to local systems, while Deligne, who gave his general equidistribution theorem after proving the Riemann hypothesis part of the Weil conjectures, established the importance of the monodromy groups of these local systems. Deligne’s theorem shows that the monodromy group of the local system incarnating a given family of exponential sums determines key statistical properties of the family of exponential sums in question. Despite the apparent simplicity of this relation of monodromy groups to statistical properties, the actual determination of the monodromy group in any particular situation is highly nontrivial and leads to many interesting questions.This book is devoted to the determination of the monodromy groups attached to various explicit families of exponential sums, especially those attached to hypergeometric sheaves, arguably the simplest local systems on G_m, and to some simple (in the sense of simple to write down) one-parameter families of one-variable sums. These last families turn out to have surprising connections to hypergeometric sheaves. One of the main technical advances of this book is to bring to bear a group-theoretic condition (S+), which, when it applies, implies very strong structural constraints on the monodromy group, and to show that (S+) does indeed apply to the monodromy groups of most hypergeometric sheaves.

Del 31 - Developments in Mathematics

Quadratic and Higher Degree Forms

AvKrishnaswami Alladi,Manjul Bhargavam. fl.

Inbunden, Engelska, 2013

1 512 kr

Skickas inom 10-15 vardagar

In the last decade, the areas of quadratic and higher degree forms have witnessed dramatic advances. This volume is an outgrowth of three seminal conferences on these topics held in 2009, two at the University of Florida and one at the Arizona Winter School. The volume also includes papers from the two focused weeks on quadratic forms and integral lattices at the University of Florida in 2010.Topics discussed include the links between quadratic forms and automorphic forms, representation of integers and forms by quadratic forms, connections between quadratic forms and lattices, and algorithms for quaternion algebras and quadratic forms. The book will be of interest to graduate students and mathematicians wishing to study quadratic and higher degree forms, as well as to established researchers in these areas. Quadratic and Higher Degree Forms contains research and semi-expository papers that stem from the presentations at conferences at the University of Florida as well as survey lectures on quadratic forms based on the instructional workshop for graduate students held at the Arizona Winter School. The survey papers in the volume provide an excellent introduction to various aspects of the theory of quadratic forms starting from the basic concepts and provide a glimpse of some of the exciting questions currently being investigated. The research and expository papers present the latest advances on quadratic and higher degree forms and their connections with various branches of mathematics.

Quadratic and Higher Degree Forms

AvPham Huu Tiep,David Savittm. fl.

E-bok

PDF, Engelska, 2013

1 825 kr

Läs direkt efter köp

In the last decade, the areas of quadratic and higher degree forms have witnessed dramatic advances. This volume is an outgrowth of three seminal conferences on these topics held in 2009, two at the University of Florida and one at the Arizona Winter School. The volume also includes papers from the two focused weeks on quadratic forms and integral lattices at the University of Florida in 2010.Topics discussed include the links between quadratic forms and automorphic forms, representation of integers and forms by quadratic forms, connections between quadratic forms and lattices, and algorithms for quaternion algebras and quadratic forms. The book will be of interest to graduate students and mathematicians wishing to study quadratic and higher degree forms, as well as to established researchers in these areas.

Quadratic and Higher Degree Forms contains research and semi-expository papers that stem from the presentations at conferences at the University of Florida as well as survey lectures on quadratic forms based on the instructional workshop for graduate students held at the Arizona Winter School. The survey papers in the volume provide an excellent introduction to various aspects of the theory of quadratic forms starting from the basic concepts and provide a glimpse of some of the exciting questions currently being investigated. The research and expository papers present the latest advances on quadratic and higher degree forms and their connections with various branches of mathematics.

Rigid Local Systems and Sporadic Simple Groups

AvNicholas Michael Katz,Antonio Rojas-Leonm. fl.

Häftad, Engelska, 2025

987 kr

Skickas inom 5-8 vardagar

The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.

Del 31 - Developments in Mathematics

Quadratic and Higher Degree Forms

AvKrishnaswami Alladi,Manjul Bhargavam. fl.

Häftad, Engelska, 2015

1 512 kr

Skickas inom 10-15 vardagar

In the last decade, the areas of quadratic and higher degree forms have witnessed dramatic advances. This volume is an outgrowth of three seminal conferences on these topics held in 2009, two at the University of Florida and one at the Arizona Winter School. The volume also includes papers from the two focused weeks on quadratic forms and integral lattices at the University of Florida in 2010.Topics discussed include the links between quadratic forms and automorphic forms, representation of integers and forms by quadratic forms, connections between quadratic forms and lattices, and algorithms for quaternion algebras and quadratic forms. The book will be of interest to graduate students and mathematicians wishing to study quadratic and higher degree forms, as well as to established researchers in these areas. Quadratic and Higher Degree Forms contains research and semi-expository papers that stem from the presentations at conferences at the University of Florida as well as survey lectures on quadratic forms based on the instructional workshop for graduate students held at the Arizona Winter School. The survey papers in the volume provide an excellent introduction to various aspects of the theory of quadratic forms starting from the basic concepts and provide a glimpse of some of the exciting questions currently being investigated. The research and expository papers present the latest advances on quadratic and higher degree forms and their connections with various branches of mathematics.

Del 15 - De Gruyter Expositions in Mathematics

Orthogonal Decompositions and Integral Lattices

AvAlexei Kostrikin,Pham Huu Tiep

Inbunden, Engelska, 1994

2 648 kr

Skickas inom 5-8 vardagar

No detailed description available for "Orthogonal Decompositions and Integral Lattices".

Finite Groups 2003

Proceedings of the Gainesville Conference on Finite Groups, March 6 - 12, 2003

AvChat Yin Ho,Peter Sinm. fl.

Inbunden, Engelska, 2004

3 984 kr

Skickas inom 5-8 vardagar

This is a volume of research articles related to finite groups. Topics covered include the classification of finite simple groups, the theory of p-groups, cohomology of groups, representation theory and the theory of buildings and geometries.As well as more than twenty original papers on the latest developments, which will be of great interest to specialists, the volume contains several expository articles, from which students and non-experts can learn about the present state of knowledge and promising directions for further research.The Finite Groups 2003 conference was held in honor of John Thompson. The profound influence of his fundamental contributions is clearly visible in this collection of papers dedicated to him.

Finite Groups 2003

Proceedings of the Gainesville Conference on Finite Groups, March 6 - 12, 2003

AvAlexandre Turull,Pham Huu Tiepm. fl.

E-bok

PDF, Engelska, 2008

4 028 kr

Läs direkt efter köp

This is a volume of research articles related to finite groups. Topics covered include the classification of finite simple groups, the theory of p-groups, cohomology of groups, representation theory and the theory of buildings and geometries.

As well as more than twenty original papers on the latest developments, which will be of great interest to specialists, the volume contains several expository articles, from which students and non-experts can learn about the present state of knowledge and promising directions for further research.

The Finite Groups 2003 conference was held in honor of John Thompson. The profound influence of his fundamental contributions is clearly visible in this collection of papers dedicated to him.

Orthogonal Decompositions and Integral Lattices

AvPham Huu Tiep,Alexei Kostrikin

E-bok

PDF, Engelska, 2011

2 425 kr

Läs direkt efter köp

No detailed description available for "e;Orthogonal Decompositions and Integral Lattices"e;.

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Pham Huu Tiep – författare

Exponential Sums, Hypergeometric Sheaves, and Monodromy Groups

Exponential Sums, Hypergeometric Sheaves, and Monodromy Groups

Quadratic and Higher Degree Forms

Quadratic and Higher Degree Forms

Rigid Local Systems and Sporadic Simple Groups

Quadratic and Higher Degree Forms

Orthogonal Decompositions and Integral Lattices

Finite Groups 2003

Finite Groups 2003

Orthogonal Decompositions and Integral Lattices

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