## 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.

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**3734**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.

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**7637**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.

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**8280**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 ...

(

**7990**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.

(

**9020**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.

(

**8312**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.

(

**9482**views)

**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.

(

**10562**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.

(

**11350**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.

(

**11179**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.

(

**11778**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.

(

**12603**views)