Arithmetic Aspects of the Theta Correspondence and Periods of Modular Forms
We review some recent results on the arithmetic of the theta correspondence for certain symplectic-orthogonal dual pairs and some applications to periods and congruences of modular forms. We also propose an integral version of a conjecture on Petersson inner products of modular forms on quaternion algebras over totally real fields.
KeywordsModular Form Elliptic Curf Automorphic Form Discrete Series Quaternion Algebra
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