Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions, and Schur Functions
ISBN: 9781441952134 / Angielski / Miękka / 143 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. The problem of representing an integer as a sum of squares of integers is one of the oldest and most significant in mathematics. It goes back at least 2000 years to Diophantus, and continues more recently with the works of Fermat, Euler, Lagrange, Jacobi, Glaisher, Ramanujan, Hardy, Mordell, Andrews, and others. Jacobi's elliptic function approach dates from his epic Fundamenta Nova of 1829. Here, the author employs his combinatorial/elliptic function methods to derive many infinite families of explicit exact formulas involving either squares or triangular numbers, two of which... The problem of representing an integer as a sum of squares of integers is one of the oldest and most significant in mathematics. It goes back at le... |
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194,97 zł |
Tauberian Theory: A Century of Developments
ISBN: 9783642059193 / Angielski / Miękka / 483 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Tauberian theory compares summability methods for series and integrals, helps to decide when there is convergence, and provides asymptotic and remainder estimates. The author shows the development of the theory from the beginning and his expert commentary evokes the excitement surrounding the early results. He shows the fascination of the difficult Hardy-Littlewood theorems and of an unexpected simple proof, and extolls Wiener's breakthrough based on Fourier theory. There are the spectacular "high-indices" theorems and Karamata's "regular variation," which permeates probability theory. The... Tauberian theory compares summability methods for series and integrals, helps to decide when there is convergence, and provides asymptotic and rema... |
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506,99 zł |
Limit Theorems for the Riemann Zeta-Function
ISBN: 9789048146475 / Angielski / Miękka / 306 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. This volume presents a wide range of results in analytic and probabilistic number theory. The full spectrum of limit theorems in the sense of weak convergence of probability measures for the modules of the Riemann zeta-function and other functions is given by Dirichlet series. Applications to the universality and functional independence of such functions are also given. Furthermore, similar results are presented for Dirichlet L-functions and Dirichlet series with multiplicative coefficients. Audience: This is a self-contained book, useful for researchers and graduate students working in...
This volume presents a wide range of results in analytic and probabilistic number theory. The full spectrum of limit theorems in the sense of weak con...
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623,99 zł |
The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics
ISBN: 9780062064011 / Angielski / Miękka / 368 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Inthe tradition of Fermat's Enigma and Pi, Marcus du Sautoy tells the illuminating, authoritative, and engagingstory of Bernhard Reimann and the ongoing quest tocapture the holy grail of mathematics--the formula to predict prime numbers.Oliver Sacks, author of The Man Who Mistook His Wife for a Hat, calls TheMusic of the Primes "an amazing book. . . . I could not put it down once Ihad started." Simon Winchester, author of The Professor and the Madman, writes, "this fascinating account, decoding the inscrutable language of themathematical...
Inthe tradition of Fermat's Enigma and Pi, Marcus du Sautoy tells the illuminating, authoritative, and engagingstory of Bernhard Rei...
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77,26 zł |
P-Adic Automorphic Forms on Shimura Varieties
ISBN: 9781441919236 / Angielski / Miękka / 390 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. In the early years of the 1980s, while I was visiting the Institute for Ad- vanced Study (lAS) at Princeton as a postdoctoral member, I got a fascinating view, studying congruence modulo a prime among elliptic modular forms, that an automorphic L-function of a given algebraic group G should have a canon- ical p-adic counterpart of several variables. I immediately decided to find out the reason behind this phenomenon and to develop the theory of ordinary p-adic automorphic forms, allocating 10 to 15 years from that point, putting off the intended arithmetic study of Shimura varieties via...
In the early years of the 1980s, while I was visiting the Institute for Ad- vanced Study (lAS) at Princeton as a postdoctoral member, I got a fascinat...
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780,00 zł |
Automorphe Formen
ISBN: 9783642123894 / Niemiecki / Miękka / 252 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Das Buch bietet eine Einfuhrung in die Theorie der automorphen Formen. Beginnend bei klassischen Modulformen fuhrt der Autor seine Leser hin zur modernen, darstellungstheoretischen Beschreibung von automorphen Formen und ihren L-Funktionen. Das Hauptgewicht legt er auf den Ubergang von der klassischen, elementaren Sichtweise zu der modernen, durch die Darstellungstheorie begrundete Herangehensweise. Diese Art der Verbindung von klassischer und moderner Sichtweise war in der Lehrbuchliteratur bisher nicht zu finden."
Das Buch bietet eine Einfuhrung in die Theorie der automorphen Formen. Beginnend bei klassischen Modulformen fuhrt der Autor seine Leser hin zur moder...
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cena:
109,33 zł |
Einführung in Die Zahlentheorie Und Algebra
ISBN: 9783834814616 / Niemiecki / Miękka / 308 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Eine kombinierte Einfuhrung in die Algebra bis zur Galoistheorie und ihren klassischen Anwendungen sowie in die Zahlentheorie: Dabei profitiert die Algebra von den Motivationen und dem reichen Beispielmaterial der Zahlentheorie; letztere gewinnt an Klarheit und Kurze durch Strukturen und Satze der Algebra. Es wird solides Grundwissen fur beide Gebiete vermittelt und gleichzeitig die Brucke zu neuesten Entwicklungen geschlagen (z. B. diophantische Probleme, Faktorisierungsmethoden, inverses Problem der Galoistheorie).
Die Neuauflage enthalt neben Korrekturen und Aktualisierungen... Eine kombinierte Einfuhrung in die Algebra bis zur Galoistheorie und ihren klassischen Anwendungen sowie in die Zahlentheorie: Dabei profitiert die Al...
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120,25 zł |
Contributions to the Founding of the Theory of Transfinite Numbers
ISBN: 9781891396533 / Angielski / Miękka / 222 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. |
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61,34 zł |
Groups Acting on Hyperbolic Space: Harmonic Analysis and Number Theory
ISBN: 9783642083020 / Angielski / Miękka / 524 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. This book is concerned with discontinuous groups of motions of the unique connected and simply connected Riemannian 3-manifold of constant curva- ture -1, which is traditionally called hyperbolic 3-space. This space is the 3-dimensional instance of an analogous Riemannian manifold which exists uniquely in every dimension n:::: 2. The hyperbolic spaces appeared first in the work of Lobachevski in the first half of the 19th century. Very early in the last century the group of isometries of these spaces was studied by Steiner, when he looked at the group generated by the inversions in spheres....
This book is concerned with discontinuous groups of motions of the unique connected and simply connected Riemannian 3-manifold of constant curva- ture...
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506,99 zł |
Diophantine Approximation on Linear Algebraic Groups: Transcendence Properties of the Exponential Function in Several Variables
ISBN: 9783642086083 / Angielski / Miękka / 633 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. Two chapters provide complete and simplified proofs of zero estimates (due to Philippon) on linear algebraic groups. The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponen... |
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389,98 zł |
Hilbert Modular Forms
ISBN: 9783642080722 / Angielski / Miękka / 252 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Important results on the Hilbert modular group and Hilbert modular forms are introduced and described in this book. In recent times, this branch of number theory has been given more and more attention and thus the need for a comprehensive presentation of these results, previously scattered in research journal papers, has become obvious. The main aim of this book is to give a description of the singular cohomology and its Hodge decomposition including explicit formulae. The author has succeeded in giving proofs which are both elementary and complete. The book contains an introduction to...
Important results on the Hilbert modular group and Hilbert modular forms are introduced and described in this book. In recent times, this branch of nu...
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194,97 zł |
Lectures on the Geometry of Numbers
ISBN: 9783642080760 / Angielski / Miękka / 162 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Carl Ludwig Siegel gave a course of lectures on the Geometry of Numbers at New York University during the academic year 1945-46, when there were hardly any books on the subject other than Minkowski's original one. This volume stems from Siegel's requirements of accuracy in detail, both in the text and in the illustrations, but involving no changes in the structure and style of the lectures as originally delivered. This book is an enticing introduction to Minkowski's great work. It also reveals the workings of a remarkable mind, such as Siegel's with its precision and power and aesthetic...
Carl Ludwig Siegel gave a course of lectures on the Geometry of Numbers at New York University during the academic year 1945-46, when there were hardl...
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194,97 zł |
Modular Units
ISBN: 9781441928139 / Angielski / Miękka / 360 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. In the present book, we have put together the basic theory of the units and cuspidal divisor class group in the modular function fields, developed over the past few years. Let i) be the upper half plane, and N a positive integer. Let r(N) be the subgroup of SL (Z) consisting of those matrices == 1 mod N. Then r(N)i) 2 is complex analytic isomorphic to an affine curve YeN), whose compactifi cation is called the modular curve X(N). The affine ring of regular functions on yeN) over C is the integral closure of C j] in the function field of X(N) over C. Here j is the classical modular function....
In the present book, we have put together the basic theory of the units and cuspidal divisor class group in the modular function fields, developed ove...
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780,00 zł |
Fundamentals of Diophantine Geometry
ISBN: 9781441928184 / Angielski / Miękka / 370 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Diophantine problems represent some of the strongest aesthetic attractions to algebraic geometry. They consist in giving criteria for the existence of solutions of algebraic equations in rings and fields, and eventually for the number of such solutions. The fundamental ring of interest is the ring of ordinary integers Z, and the fundamental field of interest is the field Q of rational numbers. One discovers rapidly that to have all the technical freedom needed in handling general problems, one must consider rings and fields of finite type over the integers and rationals. Furthermore, one is...
Diophantine problems represent some of the strongest aesthetic attractions to algebraic geometry. They consist in giving criteria for the existence of...
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311,98 zł |
The Classical Groups and K-Theory
ISBN: 9783642057373 / Angielski / Miękka / 578 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. It is a great satisfaction for a mathematician to witness the growth and expansion of a theory in which he has taken some part during its early years. When H. Weyl coined the words "classical groups," foremost in his mind were their connections with invariant theory, which his famous book helped to revive. Although his approach in that book was deliberately algebraic, his interest in these groups directly derived from his pioneering study of the special case in which the scalars are real or complex numbers, where for the first time he injected Topology into Lie theory. But ever since the...
It is a great satisfaction for a mathematician to witness the growth and expansion of a theory in which he has taken some part during its early years....
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428,99 zł |
Elliptic Curves: Diophantine Analysis
ISBN: 9783642057175 / Angielski / Miękka / 264 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. This book takes the view that parallel to the pure arithmetic theory over number fields lies the algebraic-geometric theory of algebraic systems, where sections play the role of rational points. The author formulates analogs of classic diophantine problems.
This book takes the view that parallel to the pure arithmetic theory over number fields lies the algebraic-geometric theory of algebraic systems, wher...
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389,98 zł |
Heights of Polynomials and Entropy in Algebraic Dynamics
ISBN: 9781849968546 / Angielski / Miękka / 212 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Arithmetic geometry and algebraic dynamical systems are flourishing areas of mathematics. Both subjects have highly technical aspects, yet both of- fer a rich supply of down-to-earth examples. Both have much to gain from each other in techniques and, more importantly, as a means for posing (and sometimes solving) outstanding problems. It is unlikely that new graduate students will have the time or the energy to master both. This book is in- tended as a starting point for either topic, but is in content no more than an invitation. We hope to show that a rich common vein of ideas permeates both...
Arithmetic geometry and algebraic dynamical systems are flourishing areas of mathematics. Both subjects have highly technical aspects, yet both of- fe...
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cena:
194,97 zł |
Weyl Group Multiple Dirichlet Series: Type a Combinatorial Theory (Am-175)
ISBN: 9780691150666 / Angielski / Miękka / 184 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these... Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series wi... |
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294,53 zł |
Reciprocity Laws: From Euler to Eisenstein
ISBN: 9783642086281 / Angielski / Miękka / 492 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. The history of reciprocity laws is a history of algebraic number theory. This is a book on reciprocity laws, and our introductory remark is placed at the beginning as a warning: in fact a reader who is acquainted with little more than a course in elementary number theory may be surprised to learn that quadratic reciprocity does - in a sense that we will explain - belong to the realm of algebraic number theory. Heeke { 348, p. 59]) has formulated this as follows: Von der Entdeckung des Reziprozitiitsgesetzes kann man die mo derne Zahlentheorie datieren. Seiner Form nach gehort es noch der...
The history of reciprocity laws is a history of algebraic number theory. This is a book on reciprocity laws, and our introductory remark is placed at ...
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cena:
545,99 zł |
Resolution of Singularities of Embedded Algebraic Surfaces
ISBN: 9783642083518 / Angielski / Miękka / 312 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. The common solutions of a finite number of polynomial equations in a finite number of variables constitute an algebraic variety. The degrees of freedom of a moving point on the variety is the dimension of the variety. A one-dimensional variety is a curve and a two-dimensional variety is a surface. A three-dimensional variety may be called asolid. Most points of a variety are simple points. Singularities are special points, or points of multiplicity greater than one. Points of multiplicity two are double points, points of multiplicity three are tripie points, and so on. A nodal point of a...
The common solutions of a finite number of polynomial equations in a finite number of variables constitute an algebraic variety. The degrees of freedo...
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cena:
389,98 zł |