PERIOD IDENTITIES OF CM FORMS ON QUATERNION ALGEBRAS

DOI10.1017/fms.2020.21zbMath1460.11070arXiv1807.09435OpenAlexW3102421656MaRDI QIDQ5112007

Charlotte Chan

Publication date: 27 May 2020

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.09435

zbMATH Keywords

Hecke charactersWaldspurger's formulaCM forms

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Cites Work

• The regularized Siegel-Weil formula (the second term identity) and the Rallis inner product formula
• Central values of \(L\)-functions over CM fields
• Howe correspondences on a \(p\)-adic field
• On the L-functions of canonical Hecke characters of imaginary quadratic fields
• Congruences of cusp forms and special values of their zeta functions
• Test vectors for linear forms
• On some explicit formulas in the theory of Weil representation
• Splitting metaplectic covers of dual reductive pairs
• Degenerate principal series representations for \(U(n,n)\)
• Generalized Heegner cycles and \(p\)-adic Rankin \(L\)-series. With an appendix by Brian Conrad
• Formal degrees and local theta correspondence
• Automorphic forms on GL (2)
• On some results of Atkin and Lehner
• Local ε-Factors and Characters of GL(2)
• Periods of Quaternionic Shimura Varieties. I.
• Local Orders, Root Numbers, and Modular Curves
• The special values of the zeta functions associated with cusp forms
• Conservation relations for local theta correspondence
• Central values of Rankin $L$-series over real quadratic fields
• Theta dichotomy for unitary groups
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