On Hermitian modular forms mod p

Kikuta, Toshiyuki; Nagaoka, Shoyu

doi:10.2969/jmsj/06310211

Cited by 11 publications

(5 citation statements)

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“…Forms of weight 14, 16, 18 For the proof of their integralities, we use (as in [5]) the correspondence between the Maass space and the Kohnen plus subspace which given by Krieg [9]. We review it briefly.…”

Section: Forms Of Weight 12mentioning

confidence: 99%

A ring of symmetric Hermitian modular forms of degree $2$ with integral Fourier coefficients

Kikuta

2019

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We determine the structure over Z of the ring of symmetric Hermitian modular forms with respect to Q( √ −1) of degree 2 (with a character), whose Fourier coefficients are integers. Namely, we give a set of generators consisting of 24 modular forms. As an application of our structure theorem, we give the Sturm bounds of such the modular forms of weight k with 4 | k, in the case p = 2, 3. We remark that the bounds for p ≥ 5 are already known.

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Section: Forms Of Weight 12mentioning

confidence: 99%

A ring of symmetric Hermitian modular forms of degree $2$ with integral Fourier coefficients

Kikuta

2019

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“…where X k (k = 10, 12) is Igusa's Siegel cusp form of weight k with integral Fourier coefficients (cf. Kikuta-Nagaoka [12]).…”

Section: Hermitian Modular Formsmentioning

confidence: 99%

Note on mod p property of Hermitian modular forms

Kikuta,

Nagaoka

2016

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The mod p kernel of the theta operator is the set of modular forms whose image of the theta operator is congruent to zero modulo a prime p. In the case of Siegel modular forms, the authors found interesting examples of such modular forms. For example, Igusa's odd weight cusp form is an element of mod 23 kernel of the theta operator. In this paper, we give some examples which represent elements in the mod p kernel of the theta operator in the case of Hermitian modular forms of degree 2.

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“…In this subsection, we introduce congruences for Hermitian modular forms. We use modular forms constructed in [14].…”

Section: The Case Of Hermitian Modular Formsmentioning

confidence: 99%