Workshop and international conference on Automorphic forms and number theory , Kozhikkod, India, 30 August - 03 September 2013, pp.1
Part 1: Workshop on Jacobi forms of lattice index
Organizers: Prof. M. Manickam, Prof. Ramakrishnan B., Prof. Nils Peter Skoruppa
Lecturers: Hatice Boylan (Istanbul Üniversitesi and MaxPlanckInstitute Bonn), Fabien Cléry (University of Siegen), NilsPeter Skoruppa
(University of Siegen and MaxPlanckInstitute Bonn)
Overview: The workshop aims to give a careful and thorough introduction into the theory of Jacobi forms of lattice index with emphasis on
explicit constructions, in particular, for low weights and maximal lattices as index. In addition, it will be shown how Jacobi forms can be used to
construct other types of automorphic forms via the socalled additive and multiplicative liftings.
Subjects:
● Basic notions: Lattices, shadows, discriminant modules, definition of Jacobi forms, discussion of the definition, first examples, functorial
properties
● Jacobi forms as theta functions: vector valued modular forms, relation between Jacobi forms and vector valued modular forms, dimension
formulas
● Explicit constructions of Jacobi forms: Taylor expansion around 0, Theta blocks, invariants of Weil representations
● Maximal lattices as index, explicit description of forms of singular and critical weight and maximal index
● Additive and multiplicative liftings, product expansionsSchedule:
Friday to Sunday: each day 3 lectures of 90 min and 60 minutes for discussions, questions and problem session