000			04465nam a22005053i 4500
001			EBC4908560
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005			20240729131330.0
006			m o d |
007			cr cnu||||||||
008			240724s1999 xx o ||||0 eng d
020			_a9781470438852 _q(electronic bk.)
020			_z9780821820308
035			_a(MiAaPQ)EBC4908560
035			_a(Au-PeEL)EBL4908560
035			_a(CaPaEBR)ebr11410101
035			_a(OCoLC)993779331
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA353.A9 H33 1999
082	0		_a515/.9
100	1		_aGray, Jeremy J.
245	1	0	_aNon-Euclidean Geometry in the Theory of Automorphic Functions.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c1999.
264		4	_c©2000.
300			_a1 online resource (109 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aHistory of Mathematics ; _vv.17
505	0		_aCover -- Title page -- Contents -- Acknowledgments -- Introduction by the Publishers of the Russian Translation -- Historical introduction -- A brief history of automorphic function theory, 1880-1930 -- Chapter I. The group of motions of the hyperbolic plane and its properly discontinuous subgroups -- Chapter II. Discontinuous groups in three geometries. Fuchsian functions -- Chapter III. Fuchsian functions -- Chapter IV. Kleinian groups and functions -- Chapter V. Algebraic functions and linear algebraic differential equations -- Chapter VI. Fuchsian groups and geodesics -- References -- Additional references -- Back Cover.
520			_aThis is the English translation of a volume originally published only in Russian and now out of print. The book was written by Jacques Hadamard on the work of Poincaré. Poincaré's creation of a theory of automorphic functions in the early 1880s was one of the most significant mathematical achievements of the nineteenth century. It directly inspired the uniformization theorem, led to a class of functions adequate to solve all linear ordinary differential equations, and focused attention on a large new class of discrete groups. It was the first significant application of non-Euclidean geometry. The implications of these discoveries continue to be important to this day in numerous different areas of mathematics. Hadamard begins with hyperbolic geometry, which he compares with plane and spherical geometry. He discusses the corresponding isometry groups, introduces the idea of discrete subgroups, and shows that the corresponding quotient spaces are manifolds. In Chapter 2 he presents the appropriate automorphic functions, in particular, Fuchsian functions. He shows how to represent Fuchsian functions as quotients, and how Fuchsian functions invariant under the same group are related, and indicates how these functions can be used to solve differential equations. Chapter 4 is devoted to the outlines of the more complicated Kleinian case. Chapter 5 discusses algebraic functions and linear algebraic differential equations, and the last chapter sketches the theory of Fuchsian groups and geodesics. This unique exposition by Hadamard offers a fascinating and intuitive introduction to the subject of automorphic functions and illuminates its connection to differential equations, a connection not often found in other texts. This volume is one of an informal sequence of works within the History of Mathematics series. Volumes in this subset, "Sources", are
520	8		_aclassical mathematical works that served as cornerstones for modern mathematical thought.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aAutomorphic functions.
650		0	_aGeometry, Non-Euclidean.
655		4	_aElectronic books.
700	1		_aShenitzer, Abe.
700	1		_aHadamard, Jacques.
776	0	8	_iPrint version: _aGray, Jeremy J. _tNon-Euclidean Geometry in the Theory of Automorphic Functions _dProvidence : American Mathematical Society,c1999 _z9780821820308
797	2		_aProQuest (Firm)
830		0	_aHistory of Mathematics
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4908560 _zClick to View
999			_c128069 _d128069