On p-adic properties of Siegel modular forms

Siegfried, Boecherer,; Nagaoka, Shoyu

doi:10.48550/arxiv.1305.0604

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“…Urban only treats the elliptic modular case in that paper, but I believe he and Skinner are working on applications of a more general theory. This work is related to a recent preprint [BoeNa13] by S. Boecherer and Shoyu Nagaoka where it is shown that Siegel modular forms of level Γ 0 (p m ) are p-adic modular forms. Moreover they show that derivatives of such Siegel modular forms are p-adic.…”

Section: Injecting Nearly-holomorphic Forms Into P-adic Modular Formsmentioning

confidence: 85%

Graded structures and differential operators on nearly holomorphic and quasimodular forms on classical groups

Panchishkin

2016

Preprint

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We wish to use graded structures [KrVu87], [Vu01] on differential operators and quasimodular forms on classical groups and show that these structures provide a tool to construct p-adic measures and p-adic L-functions on the corresponding non-archimedean weight spaces.An approach to constructions of automorphic L-functions on unitary groups and their padic avatars is presented. For an algebraic group G over a number field K these L functions are certain Euler products L(s, π, r, χ). In particular, our constructions cover the L-functions in [Shi00] via the doubling method of Piatetski-Shapiro and Rallis.A p-adic analogue of L(s, π, r, χ) is a p-adic analytic function Lp(s, π, r, χ) of p-adic arguments s ∈ Zp, χ mod p r which interpolates algebraic numbers defined through the normalized critical values L * (s, π, r, χ) of the corresponding complex analytic Lfunction. We present a method using arithmetic nearly-holomorphic forms and general quasimodular forms, related to algebraic automorphic forms. It gives a technique of constructing p-adic zeta-functions via quasi-modular forms and their Fourier coefficients.

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Section: Injecting Nearly-holomorphic Forms Into P-adic Modular Formsmentioning

confidence: 85%

Graded structures and differential operators on nearly holomorphic and quasimodular forms on classical groups

Panchishkin

2016

Preprint

View full text Add to dashboard Cite

show abstract

On p-adic properties of Siegel modular forms

Cited by 1 publication

References 0 publications

Graded structures and differential operators on nearly holomorphic and quasimodular forms on classical groups

Graded structures and differential operators on nearly holomorphic and quasimodular forms on classical groups

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