Equidistribution In Number Theory An Introduction PDF Download
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| Author | : Andrew Granville |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 356 |
| Release | : 2007-04-08 |
| Genre | : Mathematics |
| ISBN | : 1402054041 |
Download Equidistribution in Number Theory, An Introduction Book in PDF, ePub and Kindle
This set of lectures provides a structured introduction to the concept of equidistribution in number theory. This concept is of growing importance in many areas, including cryptography, zeros of L-functions, Heegner points, prime number theory, the theory of quadratic forms, and the arithmetic aspects of quantum chaos. The volume brings together leading researchers from a range of fields who reveal fascinating links between seemingly disparate areas.
| Author | : Manfred Einsiedler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 486 |
| Release | : 2010-09-11 |
| Genre | : Mathematics |
| ISBN | : 0857290215 |
Download Ergodic Theory Book in PDF, ePub and Kindle
This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.
| Author | : Henryk Iwaniec |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 615 |
| Release | : 2021-10-14 |
| Genre | : Education |
| ISBN | : 1470467704 |
Download Analytic Number Theory Book in PDF, ePub and Kindle
Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results. One of the primary attractions of this theory is its vast diversity of concepts and methods. The main goals of this book are to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, beautiful theorems, and powerful techniques. The book is written with graduate students in mind, and the authors nicely balance clarity, completeness, and generality. The exercises in each section serve dual purposes, some intended to improve readers' understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much of the necessary information about them included in two survey chapters.
| Author | : Nicholas M. Katz |
| Publisher | : Princeton University Press |
| Total Pages | : 212 |
| Release | : 2012-01-24 |
| Genre | : Mathematics |
| ISBN | : 0691153310 |
Download Convolution and Equidistribution Book in PDF, ePub and Kindle
Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new directions in the subject. The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters. The basic question considered in the book is how the values of the Mellin transform are distributed (in a probabilistic sense), in cases where the input function is suitably algebro-geometric. This question is answered by the book's main theorem, using a mixture of geometric, categorical, and group-theoretic methods. By providing a new framework for studying Mellin transforms over finite fields, this book opens up a new way for researchers to further explore the subject.
| Author | : Pierre Houde |
| Publisher | : |
| Total Pages | : 96 |
| Release | : 1973 |
| Genre | : Algebraic number theory |
| ISBN | : |
Download Equidistribution and L-functions in Number Theory Book in PDF, ePub and Kindle
| Author | : Emmanuel Peyre |
| Publisher | : Birkhäuser |
| Total Pages | : 455 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034883684 |
Download Rational Points on Algebraic Varieties Book in PDF, ePub and Kindle
This book is devoted to the study of rational and integral points on higher-dimensional algebraic varieties. It contains carefully selected research papers addressing the arithmetic geometry of varieties which are not of general type, with an emphasis on how rational points are distributed with respect to the classical, Zariski and adelic topologies. The present volume gives a glimpse of the state of the art of this rapidly expanding domain in arithmetic geometry. The techniques involve explicit geometric constructions, ideas from the minimal model program in algebraic geometry as well as analytic number theory and harmonic analysis on adelic groups.
| Author | : Emmanuel Kowalski |
| Publisher | : Cambridge University Press |
| Total Pages | : 271 |
| Release | : 2021-05-06 |
| Genre | : Mathematics |
| ISBN | : 1108899560 |
Download An Introduction to Probabilistic Number Theory Book in PDF, ePub and Kindle
Despite its seemingly deterministic nature, the study of whole numbers, especially prime numbers, has many interactions with probability theory, the theory of random processes and events. This surprising connection was first discovered around 1920, but in recent years the links have become much deeper and better understood. Aimed at beginning graduate students, this textbook is the first to explain some of the most modern parts of the story. Such topics include the Chebychev bias, universality of the Riemann zeta function, exponential sums and the bewitching shapes known as Kloosterman paths. Emphasis is given throughout to probabilistic ideas in the arguments, not just the final statements, and the focus is on key examples over technicalities. The book develops probabilistic number theory from scratch, with short appendices summarizing the most important background results from number theory, analysis and probability, making it a readable and incisive introduction to this beautiful area of mathematics.
| Author | : Andrew Browder |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 348 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461207150 |
Download Mathematical Analysis Book in PDF, ePub and Kindle
Among the traditional purposes of such an introductory course is the training of a student in the conventions of pure mathematics: acquiring a feeling for what is considered a proof, and supplying literate written arguments to support mathematical propositions. To this extent, more than one proof is included for a theorem - where this is considered beneficial - so as to stimulate the students' reasoning for alternate approaches and ideas. The second half of this book, and consequently the second semester, covers differentiation and integration, as well as the connection between these concepts, as displayed in the general theorem of Stokes. Also included are some beautiful applications of this theory, such as Brouwer's fixed point theorem, and the Dirichlet principle for harmonic functions. Throughout, reference is made to earlier sections, so as to reinforce the main ideas by repetition. Unique in its applications to some topics not usually covered at this level.
| Author | : Houde, Pierre |
| Publisher | : 1972 [1973] |
| Total Pages | : 96 |
| Release | : 1972 |
| Genre | : Algebraic number theory |
| ISBN | : |
Download Equidistribution and L-functions in Number Theory Book in PDF, ePub and Kindle
| Author | : Emmanuel Kowalski |
| Publisher | : Cambridge University Press |
| Total Pages | : 271 |
| Release | : 2021-05-06 |
| Genre | : Mathematics |
| ISBN | : 1108840965 |
Download An Introduction to Probabilistic Number Theory Book in PDF, ePub and Kindle
This introductory textbook for graduate students presents modern developments in probabilistic number theory, many for the first time.
