000			03024nam a22004695i 4500
001			978-3-642-29302-3
003			DE-He213
005			20140220083315.0
007			cr nn 008mamaa
008			130220s2012 gw | s |||| 0|eng d
020			_a9783642293023 _9978-3-642-29302-3
024	7		_a10.1007/978-3-642-29302-3 _2doi
050		4	_aQA241-247.5
072		7	_aPBH _2bicssc
072		7	_aMAT022000 _2bisacsh
082	0	4	_a512.7 _223
100	1		_aWang, Xueli. _eauthor.
245	1	0	_aModular Forms with Integral and Half-Integral Weights _h[electronic resource] / _cby Xueli Wang, Dingyi Pei.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2012.
300			_aX, 432 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aTheta Functions and Their Transformation Formulae -- Eisenstein Series -- The Modular Group and Its Subgroups -- Modular Forms with Integral Weight or Half-integral Weight -- Operators on the Space of Modular Forms -- New Forms and Old Forms.-Construction of Eisenstein Series -- Weil Representation and Shimura Lifting -- Trace Formula -- Integers Represented by Positive Definite Quadratic Forms.
520			_a"Modular Forms with Integral and Half-Integral Weights" focuses on the fundamental theory of modular forms of one variable with integral and half-integral weights. The main theme of the book is the theory of Eisenstein series. It is a fundamental problem to construct a basis of the orthogonal complement of the space of cusp forms; as is well known, this space is spanned by Eisenstein series for any weight greater than or equal to 2. The book proves that the conclusion holds true for weight 3/2 by explicitly constructing a basis of the orthogonal complement of the space of cusp forms. The problem for weight 1/2, which was solved by Serre and Stark, will also be discussed in this book. The book provides readers not only basic knowledge on this topic but also a general survey of modern investigation methods of modular forms with integral and half-integral weights. It will be of significant interest to researchers and practitioners in modular forms of mathematics. Dr. Xueli Wang is a Professor at South China Normal University, China. Dingyi Pei is a Professor at Guangzhou University, China.
650		0	_aMathematics.
650		0	_aGeometry, algebraic.
650		0	_aFunctions of complex variables.
650		0	_aNumber theory.
650	1	4	_aMathematics.
650	2	4	_aNumber Theory.
650	2	4	_aAlgebraic Geometry.
650	2	4	_aFunctions of a Complex Variable.
700	1		_aPei, Dingyi. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642293016
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-29302-3
912			_aZDB-2-SMA
999			_c103004 _d103004