000 | 03319nam a22005055i 4500 | ||
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001 | 978-3-540-48193-5 | ||
003 | DE-He213 | ||
005 | 20190213151551.0 | ||
007 | cr nn 008mamaa | ||
008 | 121227s1993 gw | s |||| 0|eng d | ||
020 |
_a9783540481935 _9978-3-540-48193-5 |
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024 | 7 |
_a10.1007/BFb0077194 _2doi |
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050 | 4 | _aQA241-247.5 | |
072 | 7 |
_aPBH _2bicssc |
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072 | 7 |
_aMAT022000 _2bisacsh |
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072 | 7 |
_aPBH _2thema |
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082 | 0 | 4 |
_a512.7 _223 |
100 | 1 |
_aJorgenson, Jay A. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aBasic Analysis of Regularized Series and Products _h[electronic resource] / _cby Jay A. Jorgenson, Serge Lang. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c1993. |
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300 |
_aX, 130 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1564 |
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520 | _aAnalytic number theory and part of the spectral theory of operators (differential, pseudo-differential, elliptic, etc.) are being merged under amore general analytic theory of regularized products of certain sequences satisfying a few basic axioms. The most basic examples consist of the sequence of natural numbers, the sequence of zeros with positive imaginary part of the Riemann zeta function, and the sequence of eigenvalues, say of a positive Laplacian on a compact or certain cases of non-compact manifolds. The resulting theory is applicable to ergodic theory and dynamical systems; to the zeta and L-functions of number theory or representation theory and modular forms; to Selberg-like zeta functions; andto the theory of regularized determinants familiar in physics and other parts of mathematics. Aside from presenting a systematic account of widely scattered results, the theory also provides new results. One part of the theory deals with complex analytic properties, and another part deals with Fourier analysis. Typical examples are given. This LNM provides basic results which are and will be used in further papers, starting with a general formulation of Cram r's theorem and explicit formulas. The exposition is self-contained (except for far-reaching examples), requiring only standard knowledge of analysis. | ||
650 | 0 | _aNumber theory. | |
650 | 0 | _aGlobal analysis (Mathematics). | |
650 | 0 | _aGlobal differential geometry. | |
650 | 1 | 4 |
_aNumber Theory. _0http://scigraph.springernature.com/things/product-market-codes/M25001 |
650 | 2 | 4 |
_aAnalysis. _0http://scigraph.springernature.com/things/product-market-codes/M12007 |
650 | 2 | 4 |
_aDifferential Geometry. _0http://scigraph.springernature.com/things/product-market-codes/M21022 |
700 | 1 |
_aLang, Serge. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783662181850 |
776 | 0 | 8 |
_iPrinted edition: _z9783540574880 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1564 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/BFb0077194 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
912 | _aZDB-2-BAE | ||
999 |
_c11123 _d11123 |