Abstract In this paper, we investigate the algebraic nature of value a higher Green function on an orthogonal Shimura variety at single CM point. This is motivated by conjecture Gross and Zagier in setting functions product two modular curves. process, will study analogue harmonic Maass forms Hilbert forms, obtain results concerning arithmetic their holomorphic part Fourier coefficients. As con...

Christian Brouder Laboratoire de Minéralogie Cristallographie, CNRS UMR 7590, Universités Paris 6 et 7, IPGP, case 115, 4 place Jussieu, 75252 Paris cedex 05, France. (Dated: February 2, 2008) The hierarchy of Green functions for (quasi)degenerate systems, presented in cond-mat/0308058, is calculated in detail for the case of a system with closed shells plus a single electron in a two-fold dege...

We study the first-order formalism of pure four-dimensional SU(2) Yang–Mills theory with theta-term. We describe the Green functions associated to electric and magnetic flux operators à la ’t Hooft by means of gauge-invariant non-local operators. These Green functions are related to Witten’s invariants of four-manifolds. E-mail: [email protected] 2 E-mail: [email protected] E-mail:...

Based on the technique of derivation of a theory, presented in our recent paper [1], we investigate the properties of the derived quantum system. We show that the derived quantum system possesses the (nonanomalous) symmetries of the original one, and prove that the exact Green functions of the derived theory are expressed in terms of the semiclassically approximated Green functions of the origi...