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Field name	Details
Dewey Class	512.7
Title	Arithmetic Tales ([Ebook]) / by Olivier Bordellès
Author	Bordellès, Olivier
Other name(s)	SpringerLink (Online service)
Publication	London : Springer London
Publication	, 2012.
Physical Details	XXI, 556 p. 5 illus. : online resource.
Series	Universitext 0172-5939
ISBN	9781447140962
Summary Note	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.Â In the past, a variety of very different techniques has been applied to further its understanding. Classical methods in analytic theory such as Mertensâ theorem and Chebyshevâs inequalities and the celebrated Prime Number Theorem give estimates for the distribution of prime numbers. Later on, multiplicative structure of integers leads toÂ 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 Tenenbaumâs theorem and the MÃ¶bius 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 itÂ will appeal to a wide target group including upper level undergraduates, doctoral and masters level students.:
Contents note	Basic Tools -- BÃ©zout and Gauss -- Prime Numbers -- Arithmetic Functions -- Integer Points Close to Smooth Curves -- Exponential Sums -- Algebraic Number Fields.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-1-4471-4096-2
Links to Related Works	Subject References: Mathematics . Mathematics, general . Number Theory . Authors: Bordellès, Olivier . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 512.7 . 512.7 (DDC 23) .

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Arithmetic Tales

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