LEADER 02549nam a2200361 i 4500 001 991002954509707536 006 m o d 007 cr |n||||||||| 008 160726s2015 sz ob 000 0 eng d 020 $a9783319129167 035 $ab14259850-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a512.7$223 084 $aAMS 11F50 084 $aAMS 11F27 084 $aLC QA243 100 1 $aBoylan, Hatice$0716391 245 10$aJacobi forms, finite quadratic modules and Weil representations over number fields$h[e-book] /$cHatice Boylan 260 $aCham [Switzerland] :$bSpringer,$c2015 300 $a1 online resource (xviii, 130 pages) 440 0$aLecture Notes in Mathematics,$x1617-9692 ;$v2130 504 $aIncludes bibliographical references 505 0 $aIntroduction ; Notations ; Finite quadratic modules ; Weil representations of finite quadratic modules ; Jacobi forms over totally real number fields ; Singular Jacobi forms ; Tables ; Glossary 520 $aThe new theory of Jacobi forms over totally real number fields introduced in this monograph is expected to give further insight into the arithmetic theory of Hilbert modular forms, its L-series, and into elliptic curves over number fields. This work is inspired by the classical theory of Jacobi forms over the rational numbers, which is an indispensable tool in the arithmetic theory of elliptic modular forms, elliptic curves, and in many other disciplines in mathematics and physics. Jacobi forms can be viewed as vector valued modular forms which take values in so-called Weil representations. Accordingly, the first two chapters develop the theory of finite quadratic modules and associated Weil representations over number fields. This part might also be interesting for those who are merely interested in the representation theory of Hilbert modular groups. One of the main applications is the complete classification of Jacobi forms of singular weight over an arbitrary totally real number field 650 0$aJacobi forms 650 0$aNumber theory 776 08$aPrinted edition:$z9783319129150 856 40$uhttp://link.springer.com/book/10.1007/978-3-319-12916-7$zAn electronic book accessible through the World Wide Web 907 $a.b14259850$b03-03-22$c26-07-16 912 $a991002954509707536 996 $aJacobi forms, finite quadratic modules and Weil representations over number fields$91388117 997 $aUNISALENTO 998 $ale013$b26-07-16$cm$d@ $e-$feng$gsz $h0$i0