000			01744nam a22002177a 4500
003			OSt
005			20241121172541.0
008			191210b ||||| |||| 00| 0 eng d
020			_a9783540505860
040			_cTata Book House _aICTS-TIFR
050			_aQA 573
100			_aEberhard Freitag
245			_aHilbert modular forms
260			_aHeidelberg: _bSpringer-Verlag, _c[c1990]
300			_a252 p
505			_a1. Introduction 2. Hilbert Modular Forms 3. Dimension Formulae 4. The Cohomology of the Hilbert Modular Group
520			_aImportant results on the Hilbert modular group and Hilbert modular forms are introduced and described in this book. In recent times, this branch of number theory has been given more and more attention and thus the need for a comprehensive presentation of these results, previously scattered in research journal papers, has become obvious. The main aim of this book is to give a description of the singular cohomology and its Hodge decomposition including explicit formulae. The author has succeeded in giving proofs which are both elementary and complete. The book contains an introduction to Hilbert modular forms, reduction theory, the trace formula and Shimizu's formulae, the work of Matsushima and Shimura, analytic continuation of Eisenstein series, the cohomology and its Hodge decomposition. Basic facts about algebraic numbers, integration, alternating differential forms and Hodge theory are included in convenient appendices so that the book can be used by students with a knowledge of complex analysis (one variable) and algebra. ---summary provided by publisher
650			_aMathematics
856			_uhttps://link.springer.com/book/10.1007/978-3-662-02638-0#toc
942			_2lcc _cBK
999			_c2913 _d2913