000			03046nam a22004575i 4500
001			978-3-0348-0166-9
003			DE-He213
005			20140220083739.0
007			cr nn 008mamaa
008			110804s2011 sz | s |||| 0|eng d
020			_a9783034801669 _9978-3-0348-0166-9
024	7		_a10.1007/978-3-0348-0166-9 _2doi
050		4	_aQA241-247.5
072		7	_aPBH _2bicssc
072		7	_aMAT022000 _2bisacsh
082	0	4	_a512.7 _223
100	1		_aUnterberger, André. _eauthor.
245	1	0	_aPseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms _h[electronic resource] / _cby André Unterberger.
264		1	_aBasel : _bSpringer Basel, _c2011.
300			_aVIII, 300p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aPseudo-Differential Operators, Theory and Applications ; _v8
505	0		_aIntroduction -- The Weyl calculus -- The Radon transformation and applications -- Automorphic functions and automorphic distributions -- A class of Poincaré series -- Spectral decomposition of the Poincaré summation process -- The totally radial Weyl calculus and arithmetic -- Should one generalize the Weyl calculus to an adelic setting? -- Index of notation -- Subject Index -- Bibliography.
520			_aPseudodifferential analysis, introduced in this book in a way adapted to the needs of number theorists, relates automorphic function theory in the hyperbolic half-plane Π to automorphic distribution theory in the plane. Spectral-theoretic questions are discussed in one or the other environment: in the latter one, the problem of decomposing automorphic functions in Π according to the spectral decomposition of the modular Laplacian gives way to the simpler one of decomposing automorphic distributions in R2 into homogeneous components. The Poincaré summation process, which consists in building automorphic distributions as series of g-transforms, for g Î SL(2;Z), of some initial function, say in S(R2), is analyzed in detail. On Π, a large class of new automorphic functions or measures is built in the same way: one of its features lies in an interpretation, as a spectral density, of the restriction of the zeta function to any line within the critical strip. The book is addressed to a wide audience of advanced graduate students and researchers working in analytic number theory or pseudo-differential analysis.
650		0	_aMathematics.
650		0	_aOperator theory.
650		0	_aNumber theory.
650	1	4	_aMathematics.
650	2	4	_aNumber Theory.
650	2	4	_aOperator Theory.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783034801652
830		0	_aPseudo-Differential Operators, Theory and Applications ; _v8
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-0348-0166-9
912			_aZDB-2-SMA
999			_c106608 _d106608