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Analytic Number Theory

e-books in Analytic Number Theory category

Book cover: Analytic Number TheoryAnalytic Number Theory
by - viXra ,
The aim of this paper is to present some topics in analytic number theory: classical results in prime number theory, the Dirichlet's theorem on primes in arithmetic progressions, the analytic proof of the prime number theorem by D. J. Newman, etc.
(2382 views)
Book cover: Lectures on Analytic Number TheoryLectures on Analytic Number Theory
by - Tata Institute of Fundamental Research ,
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. Contents: Formal Power Series; Analysis; Analytic theory of partitions; Representation by squares.
(3168 views)
Book cover: Lectures on a Method in the Theory of Exponential SumsLectures on a Method in the Theory of Exponential Sums
by - Tata Institute of Fundamental Research ,
The author presents a selfcontained introduction to summation and transformation formulae for exponential sums involving either the divisor function d(n) or the Fourier coefficients of a cusp form; these two cases are in fact closely analogous.
(3815 views)

Book cover: Lectures on Sieve Methods and Prime Number TheoryLectures on Sieve Methods and Prime Number Theory
by - Tata Institute of Fundamental Research ,
The aim of these lectures is to introduce the readers to the most fascinating aspects of the fruitful unifications of sieve methods and analytical means which made possible such deep developments in prime number theory ...
(3975 views)
Book cover: Lectures on Forms of Higher DegreeLectures on Forms of Higher Degree
by - Tata Institute of Fundamental Research ,
One of the principal objectives of modern number theory must be to develop the theory of forms of degree more than two,to the same satisfactory level in which the theory of quadratic forms is found today as the work of eminent mathematicians.
(4148 views)
Book cover: Lectures on Sieve MethodsLectures on Sieve Methods
by - Tata Institute of Fundamental Research ,
The aim of this text is to provide an introduction to modern sieve methods, i.e. to various forms of both the large sieve (part I of the book) and the small sieve (part II), as well as their interconnections and applications.
(3988 views)
Book cover: On Advanced Analytic Number TheoryOn Advanced Analytic Number Theory
by - Tata Institute of Fundamental Research ,
During the winter semester 1959/60, the author delivered a series of lectures on Analytic Number Theory. It was his aim to introduce his hearers to some of the important and beautiful ideas which were developed by L. Kronecker and E. Hecke.
(4878 views)
Book cover: Introduction to Analytic Number TheoryIntroduction to Analytic Number Theory
by - University of Illinois ,
Contents: Primes and the Fundamental Theorem of Arithmetic; Arithmetic functions (Elementary theory, Asymptotic estimates, Dirichlet series and Euler products); Distribution of primes; Primes in arithmetic progressions - Dirichlet's Theorem.
(5602 views)
Book cover: Lectures on The Riemann Zeta-FunctionLectures on The Riemann Zeta-Function
by - Tata Institute of Fundamental Research ,
These notes provide an intorduction to the theory of the Riemann Zeta-function for students who might later want to do research on the subject. The Prime Number Theorem, Hardy's theorem, and Hamburger's theorem are the principal results proved here.
(6431 views)
Book cover: Analytic Number Theory: A Tribute to Gauss and DirichletAnalytic Number Theory: A Tribute to Gauss and Dirichlet
by - American Mathematical Society ,
The volume begins with a definitive summary of the life and work of Dirichlet and continues with thirteen papers by leading experts on research topics of current interest in number theory that were directly influenced by Gauss and Dirichlet.
(6520 views)
Book cover: Diophantine AnalysisDiophantine Analysis
by - John Wiley & Sons ,
The author's purpose has been to supply the reader with a convenient introduction to Diophantine Analysis. No attempt has been made to include all special results, but a large number of them are to be found both in the text and in the exercises.
(6932 views)
Book cover: Distribution of Prime NumbersDistribution of Prime Numbers
by - Macquarie University ,
These notes were used by the author at Imperial College, University of London. The contents: arithmetic functions, elementary prime number theory, Dirichlet series, primes in arithmetic progressions, prime number theorem, Riemann zeta function.
(7952 views)