Proceedings of the "Segundas Jornadas de Teoría de Números"
Author: Pedro Berrizbeitia
Publisher:
Published: 2008
Total Pages: 260
ISBN-13: 9788461280070
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Author: Pedro Berrizbeitia
Publisher:
Published: 2008
Total Pages: 260
ISBN-13: 9788461280070
DOWNLOAD EBOOKAuthor: Josep Gonzalez
Publisher:
Published: 2005
Total Pages: 244
ISBN-13:
DOWNLOAD EBOOKAuthor: Álvaro Lozano-Robledo
Publisher: American Mathematical Soc.
Published: 2019-03-21
Total Pages: 506
ISBN-13: 147045016X
DOWNLOAD EBOOKGeometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.
Author: Andrej Dujella
Publisher: Springer Nature
Published:
Total Pages: 343
ISBN-13: 3031567242
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Publisher:
Published: 2011
Total Pages: 772
ISBN-13:
DOWNLOAD EBOOKAuthor:
Publisher:
Published: 2007
Total Pages: 244
ISBN-13:
DOWNLOAD EBOOKAuthor: Olivier Bordellès
Publisher: Springer Nature
Published: 2020-11-26
Total Pages: 782
ISBN-13: 3030549461
DOWNLOAD EBOOKThis textbook covers a wide array of topics in analytic and multiplicative number theory, suitable for graduate level courses. Extensively revised and extended, this Advanced Edition takes a deeper dive into the subject, with the elementary topics of the previous edition making way for a fuller treatment of more advanced topics. The core themes of the distribution of prime numbers, arithmetic functions, lattice points, exponential sums and number fields now contain many more details and additional topics. In addition to covering a range of classical and standard results, some recent work on a variety of topics is discussed in the book, including arithmetic functions of several variables, bounded gaps between prime numbers à la Yitang Zhang, Mordell's method for exponential sums over finite fields, the resonance method for the Riemann zeta function, the Hooley divisor function, and many others. Throughout the book, the emphasis is on explicit results. Assuming only familiarity with elementary number theory and analysis at an undergraduate level, this textbook provides an accessible gateway to a rich and active area of number theory. With an abundance of new topics and 50% more exercises, all with solutions, it is now an even better guide for independent study.
Author: Jörn Steuding
Publisher: Springer
Published: 2007-05-26
Total Pages: 320
ISBN-13: 3540448225
DOWNLOAD EBOOKThese notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. Universality has a strong impact on the zero-distribution: Riemann’s hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. The text proves universality for polynomial Euler products. The authors’ approach follows mainly Bagchi's probabilistic method. Discussion touches on related topics: almost periodicity, density estimates, Nevanlinna theory, and functional independence.
Author: Karen Marie Mokate
Publisher: IDB
Published: 2004
Total Pages: 368
ISBN-13: 9781931003940
DOWNLOAD EBOOKAuthor: National Library of Medicine (U.S.)
Publisher:
Published: 1982
Total Pages: 1068
ISBN-13:
DOWNLOAD EBOOKFirst multi-year cumulation covers six years: 1965-70.