id: 05686626
dt: b
an: 2012a.00445
au: Duverney, Daniel
ti: Number theory. An elementary introduction through Diophantine problems.
so: Monographs in Number Theory 4. Hackensack, NJ: World Scientific (ISBN
978-981-4307-45-1/hbk; 978-981-4307-46-8/pbk). xii, 335~p. (2010).
py: 2010
pu: Hackensack, NJ: World Scientific
la: EN
cc: F65
ut: Diophantine problems; quadratic fields; algebraic numbers
ci:
li:
ab: A very “fresh" look into Number Theory and especially into diophantine
problems, through a very interesting and appealing structure is
presented. Indeed, the structure of the content is unique and follows
five different but not always independent paths. Having as common start
the diophantine approximation the representations of real numbers,
continued fractions and Padé approximants take the lead, together with
quadratic fields and algebraic numbers. Then, the above are properly
filled up with sums of squares, arithmetical functions, number fields,
ideals and transcendence methods. The flow of the content of each
chapter is very smooth and connected, giving “delightful" results.
rv: Panayiotis Vlamos (Athens)