000			02752nam a22004695i 4500
001			978-3-642-05203-3
003			DE-He213
005			20140220084528.0
007			cr nn 008mamaa
008			100301s2010 gw | s |||| 0|eng d
020			_a9783642052033 _9978-3-642-05203-3
024	7		_a10.1007/978-3-642-05203-3 _2doi
050		4	_aQA241-247.5
072		7	_aPBH _2bicssc
072		7	_aMAT022000 _2bisacsh
082	0	4	_a512.7 _223
100	1		_aVoros, André. _eauthor.
245	1	0	_aZeta Functions over Zeros of Zeta Functions _h[electronic resource] / _cby André Voros.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2010.
300			_aXVII, 163p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aLecture Notes of the Unione Matematica Italiana, _x1862-9113 ; _v8
505	0		_aInfinite Products and Zeta-Regularization -- The Riemann Zeta Function ζ(): a Primer -- Riemann Zeros and Factorizations of the Zeta Function -- Superzeta Functions: an Overview -- Explicit Formulae -- The Family of the First Kind {ℒ ( | )} -- The Family of the Second Kind -- The Family of the Third Kind -- Extension to Other Zeta- and -Functions -- Application: an Asymptotic Criterion for the Riemann Hypothesis.
520			_aThe famous zeros of the Riemann zeta function and its generalizations (L-functions, Dedekind and Selberg zeta functions) are analyzed through several zeta functions built over those zeros. These ‘second-generation’ zeta functions have surprisingly many explicit, yet largely unnoticed properties, which are surveyed here in an accessible and synthetic manner, and then compiled in numerous tables. No previous book has addressed this neglected topic in analytic number theory. Concretely, this handbook will help anyone faced with symmetric sums over zeros like Riemann’s. More generally, it aims at reviving the interest of number theorists and complex analysts toward those unfamiliar functions, on the 150th anniversary of Riemann’s work.
650		0	_aMathematics.
650		0	_aFunctions of complex variables.
650		0	_aNumber theory.
650	1	4	_aMathematics.
650	2	4	_aNumber Theory.
650	2	4	_aFunctions of a Complex Variable.
650	2	4	_aApproximations and Expansions.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642052026
830		0	_aLecture Notes of the Unione Matematica Italiana, _x1862-9113 ; _v8
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-05203-3
912			_aZDB-2-SMA
999			_c111694 _d111694