Analytic Number Theory

e-books in Analytic Number Theory category

An Introduction to Modular Forms
by Henri Cohen - arXiv.org , 2018
Contents: Functional Equations; Elliptic Functions; Modular Forms and Functions; Hecke Operators: Ramanujan's discoveries; Euler Products, Functional Equations; Modular Forms on Subgroups of Gamma; More General Modular Forms; Some Pari/GP Commands.
(5029 views)

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.
(9325 views)

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.
(9984 views)

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 ...
(9338 views)

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.
(10427 views)

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.
(9747 views)

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.
(11017 views)

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.
(12915 views)

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.
(13058 views)

Diophantine Analysis
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.
(13254 views)

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.
(14462 views)