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Analytic Number Theory
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Analytic Number Theory
by Giuseppe Rauti - viXra , 2013
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.
Lectures on Analytic Number Theory
by H. Rademacher - Tata Institute of Fundamental Research , 1955
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.
Lectures on a Method in the Theory of Exponential Sums
by M. Jutila - Tata Institute of Fundamental Research , 1987
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.
Lectures on Sieve Methods and Prime Number Theory
by Y. Motohashi - Tata Institute of Fundamental Research , 1983
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 ...
Lectures on Forms of Higher Degree
by J.I. Igusa - Tata Institute of Fundamental Research , 1978
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.
Lectures on Sieve Methods
by H.E. Richert - Tata Institute of Fundamental Research , 1976
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.
On Advanced Analytic Number Theory
by C.L. Siegel - Tata Institute of Fundamental Research , 1961
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.
Introduction to Analytic Number Theory
by A.J. Hildebrand - University of Illinois , 2006
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.
Lectures on The Riemann Zeta-Function
by K. Chandrasekharan - Tata Institute of Fundamental Research , 1953
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.
Analytic Number Theory: A Tribute to Gauss and Dirichlet
by William Duke, Yuri Tschinkel - American Mathematical Society , 2007
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.
by R. D. Carmichael - John Wiley & Sons , 1915
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.
Distribution of Prime Numbers
by W W L Chen - Macquarie University , 2003
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.