A BÖCHERER-TYPE CONJECTURE FOR PARAMODULAR FORMS

DOI10.1142/S1793042111004629zbMath1233.11051arXiv1006.1582OpenAlexW2963058196WikidataQ122872645 ScholiaQ122872645MaRDI QIDQ3173277

Gonzalo Tornaría, Nathan C. Ryan

Publication date: 27 September 2011

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

Full work available at URL: https://arxiv.org/abs/1006.1582

zbMATH Keywords

hyperelliptic curvesSiegel modular formsquadratic twistsspecial values of \(L\)-functionsparamodular forms

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Fourier coefficients of automorphic forms (11F30) Software, source code, etc. for problems pertaining to number theory (11-04)

Related Items (6)

Fourier coefficients for twists of Siegel paramodular forms (expanded version) ⋮ The Maaß space for paramodular groups ⋮ Evaluating -functions with few known coefficients ⋮ Paramodular cusp forms ⋮ Formulas for central values of twisted spin $L$-functions attached to paramodular forms ⋮ Twisting of Siegel paramodular forms

Uses Software

• SageMath

Cites Work

• Heegner points and derivatives of \(L\)-series. II
• Jacobi forms and a certain space of modular forms
• Values of L-series of modular forms at the center of the critical strip
• The Dirichlet series of Koecher and Maaß and modular forms of weight 3/2
• Iwahori-spherical representations of \(\mathrm{GSp}(4)\) and Siegel modular forms of degree 2 with square-free level
• Some numerical computations concerning spinor zeta functions in genus $\boldsymbol{2}$ at the central point
• The fundamental lemma for the Bessel and Novodvorsky subgroups of GSp(4) II
• Computing Special Values of MotivicL-Functions
• Arithmetical lifting and its applications
• Artin's Conjecture, Turing's Method, and the Riemann Hypothesis
• Computing L-Series of Hyperelliptic Curves

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