Arithmetic Tales
Seiten
2012
|
2012 ed.
Springer London Ltd (Verlag)
978-1-4471-4095-5 (ISBN)
Springer London Ltd (Verlag)
978-1-4471-4095-5 (ISBN)
- Titel erscheint in neuer Auflage
- Artikel merken
Zu diesem Artikel existiert eine Nachauflage
This comprehensive introduction to multiplicative number theory covers counting integer points close to smooth curves and its relation to the distribution of squarefree numbers, exponential sums and algebraic number fields. Includes numerous exercises.
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 Mobius 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.
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 Mobius 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.
Basic Tools.- Bezout and Gauss.- Prime Numbers.- Arithmetic Functions.- Integer Points Close to Smooth Curves.- Exponential Sums.- Algebraic Number Fields.
| Reihe/Serie | Universitext |
|---|---|
| Übersetzer | Veronique Bordelles |
| Zusatzinfo | 5 black & white illustrations, biography |
| Verlagsort | England |
| Sprache | englisch |
| Original-Titel | Thèmes d'arithmétique |
| Maße | 156 x 234 mm |
| Gewicht | 878 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | Arithmetik |
| ISBN-10 | 1-4471-4095-8 / 1447140958 |
| ISBN-13 | 978-1-4471-4095-5 / 9781447140955 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Buch | Hardcover (2012)
Westermann Schulbuchverlag
CHF 44,90
Buch | Softcover (2018)
Gruner + Jahr (Verlag)
CHF 23,95
