Arithmetic Tales

• Olivier Bordellès
Book

Part of the Universitext book series (UTX)

1. Front Matter
Pages I-XXI
2. Olivier Bordellès
Pages 1-25
3. Olivier Bordellès
Pages 27-55
4. Olivier Bordellès
Pages 57-163
5. Olivier Bordellès
Pages 165-248
6. Olivier Bordellès
Pages 249-295
7. Olivier Bordellès
Pages 297-353
8. Olivier Bordellès
Pages 355-482
9. Back Matter
Pages 483-556

Introduction

Number theory was once famously labeled the queen of mathematics by Gauss. The multiplicative structure of the integers in particular deals with many fascinating problems some of which are easy to understand but very difficult to solve.  In the past, a variety of very different techniques has been applied to further its understanding.

Classical methods in analytic theory such as Mertens’ theorem and Chebyshev’s inequalities and the celebrated Prime Number Theorem give estimates for the distribution of prime numbers. Later on, multiplicative structure of integers leads to  multiplicative arithmetical functions for which there are many important examples in number theory. Their theory involves the Dirichlet convolution product which arises with the inclusion of several summation techniques and a survey of classical results such as Hall and Tenenbaum’s theorem and the Möbius Inversion Formula. Another topic is the counting integer points close to smooth curves and its relation to the distribution of squarefree numbers, which is rarely covered in existing texts. Final chapters focus on exponential sums and algebraic number fields. A number of exercises at varying levels are also included.

Topics in Multiplicative Number Theory introduces offers a comprehensive introduction into these topics with an emphasis on analytic number theory. Since it requires very little technical expertise it  will appeal to a wide target group including upper level undergraduates, doctoral and masters level students.

Keywords

algebraic number fields asymptotics for arithmetical functions elementary and multiplicative number theory exponential sums estimates zeta functions

Authors and affiliations

• Olivier Bordellès
• 1
1. 1.AiguilheFrance

Bibliographic information

• DOI https://doi.org/10.1007/978-1-4471-4096-2
• Copyright Information Springer-Verlag London 2012
• Publisher Name Springer, London
• eBook Packages Mathematics and Statistics
• Print ISBN 978-1-4471-4095-5
• Online ISBN 978-1-4471-4096-2
• Series Print ISSN 0172-5939
• Series Online ISSN 2191-6675