04532nam a22004937a 4500 941069 090420q2000 xxe ||| |||| 00| 0 eng d PPN13286312X 0387380329 (e-book) 9780387380322 (e-book) eng 512.7 11M36. 2010 11F72. 2010 58J35. 2010 Jorgenson, Jay, 1963- The heat kernel and theta inversion on SL (C) Jay Jorgenson, Serge Lang. 1st ed. 2008. New York, NY : Springer New York. Cham : Springer Nature, [20..]. Springer Monographs in Mathematics 2196-9922 L'impression du document génère 308 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) Bibliogr. Index Gaussians, Spherical Inversion, and the Heat Kernel -- Spherical Inversion on SL2(C) -- The Heat Gaussian and Heat Kernel -- QED, LEG, Transpose, and Casimir -- Enter ?: The General Trace Formula -- Convergence and Divergence of the Selberg Trace -- The Cuspidal and Noncuspidal Traces -- The Heat Kernel on ?\G/K -- The Fundamental Domain -- ?-Periodization of the Heat Kernel -- Heat Kernel Convolution on (?\G/K) -- Fourier-Eisenstein Eigenfunction Expansions -- The Tube Domain for ?? -- The ?/U-Fourier Expansion of Eisenstein Series -- Adjointness Formula and the ?\G-Eigenfunction Expansion -- The Eisenstein-Cuspidal Affair -- The Eisenstein Y-Asymptotics -- The Cuspidal Trace Y-Asymptotics -- Analytic Evaluations Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 The present monograph develops the fundamental ideas and results surrounding heat kernels, spectral theory, and regularized traces associated to the full modular group acting on SL2(C). The authors begin with the realization of the heat kernel on SL2(C) through spherical transform, from which one manifestation of the heat kernel on quotient spaces is obtained through group periodization. From a different point of view, one constructs the heat kernel on the group space using an eigenfunction, or spectral, expansion, which then leads to a theta function and a theta inversion formula by equating the two realizations of the heat kernel on the quotient space. The trace of the heat kernel diverges, which naturally leads to a regularization of the trace by studying Eisenstein series on the eigenfunction side and the cuspidal elements on the group periodization side. By focusing on the case of SL2(Z[i]) acting on SL2(C), the authors are able to emphasize the importance of specific examples of the general theory of the general Selberg trace formula and uncover the second step in their envisioned "ladder" of geometrically defined zeta functions, where each conjectured step would include lower level zeta functions as factors in functional equations Fonctions thêta Formules de trace Noyaux (analyse fonctionnelle) Équation de la chaleur Inversions (géométrie) Lang, Serge, 1927-2005. aut 12910342X The heat kernel and theta inversion on SL (C) Jay Jorgenson, Serge Lang 2008 New York Springer 1 vol. (X-319 p.) Springer Monographs in Mathematics 0-387-38031-0 The Heat Kernel and Theta Inversion on SL2(C) Texte imprimé 9780387564050 The Heat Kernel and Theta Inversion on SL2(C) Texte imprimé 9781441922823 PDF https://doi.org/10.1007/978-0-387-38032-2 Accès sur la plateforme de l'éditeur https://revue-sommaire.istex.fr/ark:/67375/8Q1-F9Z2F1R9-G Accès sur la plateforme Istex 452349901:747854777 https://ezproxy.univ-orleans.fr/login?url=https://dx.doi.org/10.1007/978-0-387-38032-2 Accès Université d'Orléans 180339901:750872276 https://ezproxy.insa-cvl.fr/login?qurl=https://dx.doi.org/10.1007/978-0-387-38032-2 Accès INSA CVL 941069 Livre numérique Ressource numérique INSA ENSA 0/Bibliothèque numérique/ 1/Bibliothèque numérique/Autre ressource numérique/