000 03291nam a22005415i 4500
001 978-1-4419-7847-9
003 DE-He213
005 20140220083725.0
007 cr nn 008mamaa
008 101110s2011 xxu| s |||| 0|eng d
020 _a9781441978479
_9978-1-4419-7847-9
024 7 _a10.1007/978-1-4419-7847-9
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
082 0 4 _a516.35
_223
100 1 _aFarkas, Hershel M.
_eauthor.
245 1 0 _aGeneralizations of Thomae's Formula for Zn Curves
_h[electronic resource] /
_cby Hershel M. Farkas, Shaul Zemel.
264 1 _aNew York, NY :
_bSpringer New York,
_c2011.
300 _aXVII, 354 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aDevelopments in Mathematics, Diophantine Approximation: Festschrift for Wolfgang Schmidt,
_x1389-2177 ;
_v21
505 0 _a- Introduction.- 1. Riemann Surfaces -- 2. Zn Curves -- 3. Examples of Thomae Formulae -- 4. Thomae Formulae for Nonsingular Zn Curves -- 5. Thomae Formulae for Singular Zn Curves.-6. Some More Singular Zn Curves.-Appendix A. Constructions and Generalizations for the Nonsingular and Singular Cases.-Appendix B. The Construction and Basepoint Change Formulae for the Symmetric Equation Case.-References.-List of Symbols.-Index.
520 _aThis book provides a comprehensive overview of the theory of theta functions, as applied to compact Riemann surfaces, as well as the necessary background for understanding and proving the Thomae formulae. The exposition examines the properties of a particular class of compact Riemann surfaces, i.e., the Zn curves, and thereafter focuses on how to prove the Thomae formulae, which give a relation between the algebraic parameters of the Zn curve, and the theta constants associated with the Zn curve. Graduate students in mathematics will benefit from the classical material, connecting Riemann surfaces, algebraic curves, and theta functions, while young researchers, whose interests are related to complex analysis, algebraic geometry, and number theory, will find new rich areas to explore. Mathematical physicists and physicists with interests also in conformal field theory will surely appreciate the beauty of this subject.
650 0 _aMathematics.
650 0 _aGeometry, algebraic.
650 0 _aFunctions of complex variables.
650 0 _aDifferential equations, partial.
650 0 _aFunctions, special.
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aAlgebraic Geometry.
650 2 4 _aFunctions of a Complex Variable.
650 2 4 _aSeveral Complex Variables and Analytic Spaces.
650 2 4 _aSpecial Functions.
650 2 4 _aNumber Theory.
700 1 _aZemel, Shaul.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781441978462
830 0 _aDevelopments in Mathematics, Diophantine Approximation: Festschrift for Wolfgang Schmidt,
_x1389-2177 ;
_v21
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4419-7847-9
912 _aZDB-2-SMA
999 _c105872
_d105872