| 000 | 03023nam a22004575i 4500 | ||
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| 001 | 978-3-540-39331-3 | ||
| 003 | DE-He213 | ||
| 005 | 20190213151217.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 121227s1987 gw | s |||| 0|eng d | ||
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_a9783540393313 _9978-3-540-39331-3 |
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| 024 | 7 |
_a10.1007/BFb0077696 _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 |
_aFischer, Jürgen. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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| 245 | 1 | 3 |
_aAn Approach to the Selberg Trace Formula via the Selberg Zeta-Function _h[electronic resource] / _cby Jürgen Fischer. |
| 264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c1987. |
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| 300 |
_aIV, 188 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 ; _v1253 |
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| 505 | 0 | _aBasic facts -- The trace of the iterated resolvent kernel -- The entire function ? associated with the selberg zeta-function -- The general selberg trace formula. | |
| 520 | _aThe Notes give a direct approach to the Selberg zeta-function for cofinite discrete subgroups of SL (2,#3) acting on the upper half-plane. The basic idea is to compute the trace of the iterated resolvent kernel of the hyperbolic Laplacian in order to arrive at the logarithmic derivative of the Selberg zeta-function. Previous knowledge of the Selberg trace formula is not assumed. The theory is developed for arbitrary real weights and for arbitrary multiplier systems permitting an approach to known results on classical automorphic forms without the Riemann-Roch theorem. The author's discussion of the Selberg trace formula stresses the analogy with the Riemann zeta-function. For example, the canonical factorization theorem involves an analogue of the Euler constant. Finally the general Selberg trace formula is deduced easily from the properties of the Selberg zeta-function: this is similar to the procedure in analytic number theory where the explicit formulae are deduced from the properties of the Riemann zeta-function. Apart from the basic spectral theory of the Laplacian for cofinite groups the book is self-contained and will be useful as a quick approach to the Selberg zeta-function and the Selberg trace formula. | ||
| 650 | 0 | _aNumber theory. | |
| 650 | 1 | 4 |
_aNumber Theory. _0http://scigraph.springernature.com/things/product-market-codes/M25001 |
| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer eBooks | |
| 776 | 0 | 8 |
_iPrinted edition: _z9783662183144 |
| 776 | 0 | 8 |
_iPrinted edition: _z9783540152088 |
| 830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1253 |
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| 856 | 4 | 0 | _uhttps://doi.org/10.1007/BFb0077696 |
| 912 | _aZDB-2-SMA | ||
| 912 | _aZDB-2-LNM | ||
| 912 | _aZDB-2-BAE | ||
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