Frobenius Distributions: Lang-Trotter and Sato-Tate Conjectures, David Kohel, Igor Shparlinski

Автор: Kenney Margaret J.
Название: Number Treasury 3: Investigations, Facts and Conjectures abo
ISBN: 9814603694 ISBN-13(EAN): 9789814603690
Издательство: World Scientific Publishing
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Цена: 33790.00 T
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"This book is a great choice for teachers as well as students who are interested in either recreational mathematics or in studying interesting number patterns. The activities can easily be used in both middle and secondary mathematics classrooms as enrichment topics. They would also be appropriate for use in math clubs and to challenge advanced learners. I highly recommend this book for anyone who loves exploring interesting properties of numbers."

Mathematics Teaching in the Middle School

"It is indeed an extremely rare occasion when a book can be used as a reference through such a broad level of math classes. This one is an existence proof."

Mathematical Association of America

"I recommend this book as a resource for developing lessons that extend students' understanding of the properties and relationships of numbers. The investigations allow students to make conjectures and generalizations about numbers and act as mathematicians."

Mathematics Teacher

"Many of the provided activities would be suitable for the high-school classroom, and could give students the opportunity to explore certain aspects of mathematics with a degree of independence."

Mathematical Gazette

This resource volume is an enlargement as well as an update of the previous edition. The book aims to introduce the reader to over 100 different families of positive integers. A brief historical note accompanies the descriptions and examples of several of the families together with a mix of routine exercises and problems as well as some thought provokers to solve. Number Treasury³ especially aims to stimulate further study beyond the scope of the introductory treatment given in the book. The emphasis in Number Treasury³ is on doing not proving. However, the reader is directed to think critically about situations, to provide explanations, to make generalizations, and to formulate conjectures. To engage the reader from the start, the book begins with a set of rich Investigations. These are standalone activities that represent each of the chapters of the book.

Автор: Wilfred W. J. Hulsbergen
Название: Conjectures in Arithmetic Algebraic Geometry
ISBN: 3528064331 ISBN-13(EAN): 9783528064334
Издательство: Springer
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Цена: 47880.00 T
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Описание: In this expository paper we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued mathematicians for a long period of time. Starting from Fermat's Last Theorem one is naturally led to intro- duce L-functions, the main motivation being the calculation of class numbers. In particular, Kummer showed that the class numbers of cyclotomic fields playa decisive role in the corroboration of Fermat's Last Theorem for a large class of exponents. Before Kummer, Dirich- let had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions. Another prominent appearance of an L-function is Riemann's paper where the now famous Riemann Hypothesis was stated. In short, nineteenth century number theory showed that much, if not all, of number theory is reflected by proper- ties of L-functions. Twentieth century number theory, class field theory and algebraic geometry only strengthen the nineteenth century number theorists's view. We just mention the work of E. Heeke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlet's L-functions to obtain results on the distribution of primes in number fields. Artin introduced his L-functions as a non-abelian generaliza- tion of Dirichlet's L-functions with a generalization of class field the- ory to non-abelian Galois extensions of number fields in mind. Weil introduced his zeta-function for varieties over finite fields in relation to a problem in number theory.

Автор: Benjamin Fine, Anthony Gaglione, Alexei Myasnikov,
Название: The Elementary Theory of Groups: A Guide through the Proofs of the Tarski Conjectures
ISBN: 3110341999 ISBN-13(EAN): 9783110341997
Издательство: Walter de Gruyter
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Описание: After being an open question for sixty years the Tarski conjecture was answered in the affirmative by Olga Kharlampovich and Alexei Myasnikov and independently by Zlil Sela. Both proofs involve long and complicated applications of algebraic geometry over free groups as well as an extension of methods to solve equations in free groups originally developed by Razborov. This book is an examination of the material on the general elementary theory of groups that is necessary to begin to understand the proofs. This material includes a complete exposition of the theory of fully residually free groups or limit groups as well a complete description of the algebraic geometry of free groups. Also included are introductory material on combinatorial and geometric group theory and first-order logic. There is then a short outline of the proof of the Tarski conjectures in the manner of Kharlampovich and Myasnikov.

Автор: Kenney Margaret J., Bezuszka Stanley J.
Название: Number Treasury3: Investigations, Facts and Conjectures about More Than 100 Number Families: 3rd Edition
ISBN: 9814603686 ISBN-13(EAN): 9789814603683
Издательство: World Scientific Publishing
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Цена: 65470.00 T
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Описание: This resource volume is an enlargement as well as an update of the previous edition. The book aims to introduce the reader to over 100 different families of positive integers.

Автор: Alonso-gutierrez, David Bastero, Jesus
Название: Approaching the kannan-lovasz-simonovits and variance conjectures
ISBN: 3319132628 ISBN-13(EAN): 9783319132624
Издательство: Springer
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Цена: 32600.00 T
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Описание: Focusing on two central conjectures of Asymptotic Geometric Analysis, the Kannan-Lovasz-Simonovits spectral gap conjecture and the variance conjecture, these Lecture Notes present the theory in an accessible way, so that interested readers, even those who are not experts in the field, will be able to appreciate the treated topics.

Автор: John Coates; Peter Schneider; R. Sujatha; Otmar Ve
Название: Noncommutative Iwasawa Main Conjectures over Totally Real Fields
ISBN: 3642443354 ISBN-13(EAN): 9783642443350
Издательство: Springer
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Цена: 102480.00 T
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Описание: The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives.

Автор: Gordon E. Willmot; X. Sheldon Lin
Название: Lundberg Approximations for Compound Distributions with Insurance Applications
ISBN: 0387951350 ISBN-13(EAN): 9780387951355
Издательство: Springer
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Описание: These notes represent our summary of much of the recent research that has been done in recent years on approximations and bounds that have been developed for compound distributions and related quantities which are of interest in insurance and other areas of application in applied probability.

Автор: Lennart Bondesson
Название: Generalized Gamma Convolutions and Related Classes of Distributions and Densities
ISBN: 0387978666 ISBN-13(EAN): 9780387978666
Издательство: Springer
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Описание: This work is an attempt to present the main results on this class of probability distributions and related classes in a rather logical order. Those who do not want to visit a mysterious land situated between the land of probability theory and statistics and the land of classical analysis should not look at this work.

Автор: Thomas Hawkins
Название: The Mathematics of Frobenius in Context
ISBN: 1489987002 ISBN-13(EAN): 9781489987006
Издательство: Springer
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Цена: 121110.00 T
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Описание: This book on focuses on the work of Ferdinand Frobenius in linear algebra, its relationship with the work of Burnside, Cartan, and Molien, and its extension by Schur and Brauer. Also covers the Berlin school of mathematics and the guiding force of Weierstrass.