Combinatorics of Maass-Shimura operators

DOI10.1016/j.jnt.2007.10.010zbMath1213.11098OpenAlexW2001587894MaRDI QIDQ1024423

Dominic Lanphier

Publication date: 17 June 2009

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2007.10.010

zbMATH Keywords

modular form\(L\)-functionRankin-Cohen bracketsMaass-Shimura operators

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Fourier coefficients of automorphic forms (11F30) Holomorphic modular forms of integral weight (11F11) Hecke-Petersson operators, differential operators (one variable) (11F25)

Related Items

Lowest weight modules of \(\mathrm{Sp}_4 (\mathbb{R})\) and nearly holomorphic Siegel modular forms, SOME REMARKS ON RANKIN–COHEN BRACKETS OF EIGENFORMS, Meromorphic quasi-modular forms and their \(L\)-functions, The Lie theory of certain modular form and arithmetic identities, Rankin-Cohen brackets of eigenforms and modular forms, ACTION OF <i>E</i>₂ON HECKE EIGENFORMS, Products of nearly holomorphic eigenforms, Kernels of \(L\)-functions of cusp forms, Syntomic regulators of Asai-Flach classes, Determining cuspforms from critical values of convolution L-functions and Rankin–Cohen brackets, An average of special values of Dirichlet series of Rankin-Selberg type

Uses Software

• Magma

Cites Work

• Special values and mixed weight triple products (with an appendix by Don Blasius)
• Renormalization of certain integrals defining triple product \(L\)-functions.
• The Lie theory of the Rankin-Cohen brackets and allied bi-differential operators
• A note on three lemmas of Shimura
• Sums involving the values at negative integers of \(L\)-functions of quadratic characters
• Twists of newforms and pseudo-eigenvalues of \(W\)-operators
• The special values of the zeta functions associated with Hilbert modular forms
• Modular forms and differential operators
• Differential operators, holomorphic projection, and singular forms
• The Magma algebra system. I: The user language
• Dirichlet series and automorphic forms
• The special values of the zeta functions associated with cusp forms
• The Scalar Product of Modular Forms
• Modular Forms
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