000			03535nam a22004575i 4500
001			978-0-387-72474-4
003			DE-He213
005			20161121231124.0
007			cr nn 008mamaa
008			100301s2007 xxu| s |||| 0|eng d
020			_a9780387724744 _9978-0-387-72474-4
024	7		_a10.1007/978-0-387-72474-4 _2doi
050		4	_aQA241-247.5
072		7	_aPBH _2bicssc
072		7	_aMAT022000 _2bisacsh
082	0	4	_a512.7 _223
100	1		_aShimura, Goro. _eauthor.
245	1	0	_aElementary Dirichlet Series and Modular Forms _h[electronic resource] / _cby Goro Shimura.
264		1	_aNew York, NY : _bSpringer New York, _c2007.
300			_aVIII, 152 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringer Monographs in Mathematics, _x1439-7382
505	0		_aPreliminaries on Modular Forms and Dirichlet Series -- Critical Values of Dirichlet L-functions -- The Case of Imaginary Quadratic Fields and Nearly Holomorphic Modular Forms -- Eisenstein Series -- Critical Values of Dirichlet Series Associated with Imaginary Quadratic Fields -- Supplementary Results.
520			_aThe main topics of the book are the critical values of Dirichlet L-functions and Hecke L-functions of an imaginary quadratic field, and various problems on elliptic modular forms. As to the values of Dirichlet L-functions, all previous papers and books reiterate a single old result with a single old method. After a review of elementary Fourier analysis, the author presents completely new results with new methods, though old results will also be proved. No advanced knowledge of number theory is required up to this point. As applications, new formulas for the second factor of the class number of a cyclotomic field will be given. The second half of the book assumes familiarity with basic knowledge of modular forms. However, all definitions and facts are clearly stated, and precise references are given. The notion of nearly holomorphic modular forms is introduced and applied to the determination of the critical values of Hecke L-functions of an imaginary quadratic field. Other notable features of the book are: (1) some new results on classical Eisenstein series; (2) the discussion of isomorphism classes of elliptic curves with complex multiplication in connection with their zeta function and periods; (3) a new class of holomorphic differential operators that send modular forms to those of a different weight. The book will be of interest to graduate students and researchers who are interested in special values of L-functions, class number formulae, arithmetic properties of modular forms (especially their values), and the arithmetic properties of Dirichlet series. It treats in detail, from an elementary viewpoint, the simplest cases of a fundamental area of ongoing research, the only prerequisite being a basic course in algebraic number theory.
650		0	_aMathematics.
650		0	_aAlgebraic geometry.
650		0	_aNumber theory.
650	1	4	_aMathematics.
650	2	4	_aNumber Theory.
650	2	4	_aAlgebraic Geometry.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387724737
830		0	_aSpringer Monographs in Mathematics, _x1439-7382
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-72474-4
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c508931 _d508931