LEADER 02413nam a2200325 i 4500 001 991002954579707536 008 160726s2015 sz b 000 0 eng d 020 $a9783319129150 035 $ab14259862-39ule_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 /$cHatice Boylan 260 $aCham [Switzerland] :$bSpringer,$cc2015 300 $axviii, 130 p. ;$c24 cm 440 0$aLecture notes in mathematics,$x0075-8434 ;$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 907 $a.b14259862$b22-11-16$c26-07-16 912 $a991002954579707536 945 $aLE013 11F BOY11 (2015)$g1$i2013000293721$lle013$op$pE36.39$q-$rl$s- $t0$u1$v0$w1$x0$y.i15788829$z22-11-16 996 $aJacobi forms, finite quadratic modules and Weil representations over number fields$91388117 997 $aUNISALENTO 998 $ale013$b26-07-16$cm$da $e-$feng$gsz $h0$i0