000 02859nam a22004455i 4500
001 978-1-4614-2125-2
003 DE-He213
005 20140220083245.0
007 cr nn 008mamaa
008 111117s2012 xxu| s |||| 0|eng d
020 _a9781461421252
_9978-1-4614-2125-2
024 7 _a10.1007/978-1-4614-2125-2
_2doi
050 4 _aQA297-299.4
072 7 _aPBKS
_2bicssc
072 7 _aMAT021000
_2bisacsh
072 7 _aMAT006000
_2bisacsh
082 0 4 _a518
_223
100 1 _aShimura, Goro.
_eauthor.
245 1 0 _aModular Forms: Basics and Beyond
_h[electronic resource] /
_cby Goro Shimura.
264 1 _aNew York, NY :
_bSpringer New York,
_c2012.
300 _aX, 178 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 _aPreface -- Notation and Terminology -- Chapter I. Preliminaries -- Chapter II. Theta Functions and Factors of Automorphy -- Chapter III. The Rationality and Eisenstein Series -- Chapter IV. The Correspondence between Forms of Integral and Half-integral Weight -- Chapter V. The Arithmeticity of Critical Values of Dirichlet Series -- Appendix -- References -- Index.
520 _aThis is an advanced book on modular forms. While there are many books published about modular forms, they are written at an elementary level, and not so interesting from the viewpoint of a reader who already knows the basics. This book offers something new, which may satisfy the desire of such a reader. However, we state every definition and every essential fact concerning classical modular forms of one variable. One of the principal new features of this book is the theory of modular forms of half-integral weight, another being the discussion of theta functions and Eisenstein series of holomorphic and nonholomorphic types. Thus the book is presented so that the reader can learn such theories systematically. Ultimately, we concentrate on the following two themes: (I) The correspondence between the forms of half-integral weight and those of integral weight. (II) The arithmeticity of various Dirichlet series associated with modular forms of integral or half-integral weight. Goro Shimura is currently a professor emeritus of mathematics at Princeton University.
650 0 _aMathematics.
650 0 _aNumerical analysis.
650 1 4 _aMathematics.
650 2 4 _aNumerical Analysis.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461421245
830 0 _aSpringer Monographs in Mathematics,
_x1439-7382
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-2125-2
912 _aZDB-2-SMA
999 _c101208
_d101208