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020 _a9783540481935
_9978-3-540-48193-5
024 7 _a10.1007/BFb0077194
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
072 7 _aPBH
_2thema
082 0 4 _a512.7
_223
100 1 _aJorgenson, Jay A.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
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.
300 _aX, 130 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1564
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