منابع مشابه
Harmonic Maass Forms, Mock Modular Forms, and Quantum Modular Forms
This short course is an introduction to the theory of harmonic Maass forms, mock modular forms, and quantum modular forms. These objects have many applications: black holes, Donaldson invariants, partitions and q-series, modular forms, probability theory, singular moduli, Borcherds products, central values and derivatives of modular L-functions, generalized Gross-Zagier formulae, to name a few....
متن کاملTheta lifts of Bianchi modular forms and applications to paramodularity
We explain how the work of Johnson-Leung and Roberts on lifting Hilbert modular forms for real quadratic fields to Siegel modular forms can be adapted to imaginary quadratic fields. For this, we use archimedean results from Harris, Soudry and Taylor and replace the global arguments of Roberts by the non-vanishing result of Takeda. As an application of our lifting result, we exhibit an abelian s...
متن کاملGrowth and Nonvanishing of Restricted Siegel Modular Forms Arising as Saito-kurokawa Lifts
We study the analytic behavior of the restriction of a Siegel modular form to H × H in the case that the Siegel form is a Saito-Kurokawa lift. A formula of Ichino links this behavior to a family of GL3 ×GL2 L-functions.
متن کاملSaito-kurokawa Lifts, L-values for Gl2, and Congruences between Siegel Modular Forms
Saito-Kurokawa Lifts, L-values for GL2, and Congruences Between Siegel ModularForms
متن کاملModular Forms
Here are the notes I took for Wei Zhang’s course on modular forms offered at Columbia University in Spring 2013 (MATH G4657: Algebraic Number Theory). Hopefully these notes will appear in a more complete form during Fall 2014. I recommend that you visit my website from time to time for the most updated version. Due to my own lack of understanding of the materials, I have inevitably introduced b...
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ژورنال
عنوان ژورنال: The Ramanujan Journal
سال: 2013
ISSN: 1382-4090,1572-9303
DOI: 10.1007/s11139-013-9469-z