[PDF] sons binauraux avis
[PDF] i doser
[PDF] baudelaire les fleurs du mal
[PDF] baudelaire poeme
[PDF] baudelaire influences
[PDF] bibliographie de baudelaire
[PDF] général aupick
[PDF] le peintre de la vie moderne baudelaire
[PDF] le peintre de la vie moderne eloge du maquillage
[PDF] le peintre de la vie moderne pdf
[PDF] texte maquillage
[PDF] carte ign guadeloupe gratuite
[PDF] page de garde open office télécharger
[PDF] besoin d'appartenance maslow
[PDF] contrat de prêt d'argent entre particuliers québec
[PDF] i doser
[PDF] baudelaire les fleurs du mal
[PDF] baudelaire poeme
[PDF] baudelaire influences
[PDF] bibliographie de baudelaire
[PDF] général aupick
[PDF] le peintre de la vie moderne baudelaire
[PDF] le peintre de la vie moderne eloge du maquillage
[PDF] le peintre de la vie moderne pdf
[PDF] texte maquillage
[PDF] carte ign guadeloupe gratuite
[PDF] page de garde open office télécharger
[PDF] besoin d'appartenance maslow
[PDF] contrat de prêt d'argent entre particuliers québec
![Riemann’s theta formula - University of Pennsylvania Riemann’s theta formula - University of Pennsylvania](https://pdfprof.com/Listes/17/17823-17theta-relations_v2.pdf.pdf.jpg)
Riemann"s theta formula
Ching-Li Chai
version 12/03/2014 There is a myriad of identities satisfied by the Riemann theta functionq(z;W)and its close relativesqa b(z;W). The most famous among these theta relations is a quartic relation known to Riemann, associated to a 44 orthogonal matrix with all entries1; see 1.3. It debuted as formula (12) on p.20 of [10], and was namedRiemann"s theta formulaby Prym. In the preface of [10] Prym said that he learned of this formula from Riemann in Pisa, where he was with Riemann for several weeks in early 1865, and that he wrote down a proof following Riemann"s suggestions. For any fixed abelian variety, these theta identities give a set ofquadraticequations which defines this abelian variety. The coefficients of these quadratic equations are theta constants, or "thetanullwerte", which vary with the abelian variety. At the same time, the Riemann theta identi-ties give a set ofquarticequations satisfied by the theta constants, which gives a systems of defining
equations of the moduli space of abelian varieties (endowed with suitable theta level structures). x1. Riemann"s theta formula We will first formulate a generalized Riemann theta identity, for theta functions attached to a quadratic form on a lattice. (1.1) DEFINITION. (THETA FUNCTIONS ATTACHED TO QUADRATIC FORMS)LetQbe aQ- valuedpositive definitesymmetric bilinear form on anh-dimensionalQ-vector spaceGQ, where his a positive integer. LetGGQbe aZ-lattice inGQ, i.e. a free abelian subgroup ofGQof rankh. Denote byG_QtheQ-linear dual ofGQ, and letG_:=fl2G_Qjl(G)Z:g. We identify elements ofQg QGQwithg-tuples of elements ofGQand similarly forQg QG_Q. (i) The pairingQgCg3(n;z)7!tnz2ConQgCgand the natural pairingGQG_Q!Q induces a pairingh;i:(Qg