000 03077nam a22004455i 4500
001 978-1-4471-4096-2
003 DE-He213
005 20140220083237.0
007 cr nn 008mamaa
008 120530s2012 xxk| s |||| 0|eng d
020 _a9781447140962
_9978-1-4471-4096-2
024 7 _a10.1007/978-1-4471-4096-2
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
082 0 4 _a512.7
_223
100 1 _aBordellès, Olivier.
_eauthor.
245 1 0 _aArithmetic Tales
_h[electronic resource] /
_cby Olivier Bordellès.
264 1 _aLondon :
_bSpringer London :
_bImprint: Springer,
_c2012.
300 _aXXI, 556 p. 5 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUniversitext,
_x0172-5939
505 0 _aBasic Tools -- Bézout and Gauss -- Prime Numbers -- Arithmetic Functions -- Integer Points Close to Smooth Curves -- Exponential Sums -- Algebraic Number Fields.
520 _aNumber 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.
650 0 _aMathematics.
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aNumber Theory.
650 2 4 _aMathematics, general.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781447140955
830 0 _aUniversitext,
_x0172-5939
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4471-4096-2
912 _aZDB-2-SMA
999 _c100767
_d100767