Sturm type theorem for Siegel modular forms of genus 2 modulo p

Choi, Dohoon; Choie, YoungJu; Kikuta, Toshiyuki

doi:10.4064/aa158-2-2

Cited by 16 publications

(20 citation statements)

References 17 publications

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“…Therefore we may assume a((n, r, m), f ) ∈ Z for all (n, r, m). Applying the Sturm type theorem [3] for all primes p 5, we obtain the assertion of the lemma. 1 from degree2 .…”

Section: In Order To Provementioning

confidence: 81%

On the computation of the determinant of vector-valued Siegel modular forms

Takemori¹

2014

LMS J. Comput. Math.

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Let A 0 (Γ2) denote the ring of scalar-valued Siegel modular forms of degree two, level 1 and even weights. In this paper, we prove the determinant of a basis of the module of vector-valued Siegel modular forms k≡ mod 2 A det k ⊗Sym(j) (Γ2) over A 0 (Γ2) is equal to a power of the cusp form of degree two and weight 35 up to a constant. Here j = 4, 6 and = 0, 1. The main result in this paper was conjectured by Ibukiyama (Comment. Math. Univ. St. Pauli 61 (2012) 51-75).

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“…Therefore we may assume a((n, r, m), f ) ∈ Z for all (n, r, m). Applying the Sturm type theorem [3] for all primes p 5, we obtain the assertion of the lemma. 1 from degree2 .…”

Section: In Order To Provementioning

confidence: 81%

On the computation of the determinant of vector-valued Siegel modular forms

Takemori¹

2014

LMS J. Comput. Math.

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“…Nagaoka [16]). Note that E (3) k ∈ −1 Q (E (2) k ) for any even k. We can construct F k ∈ −1 Q (X k ) (k = 10, 12) by…”

Section: Remark On S N (K )mentioning

confidence: 99%

Ramanujan type congruences for the Klingen-Eisenstein series

Kikuta

Takemori

2014

Abh. Math. Semin. Univ. Hambg.

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In the case of Siegel modular forms of degree n, we prove that, for almost all prime ideals p in any ring of algebraic integers, mod p m cusp forms are congruent to true cusp forms of the same weight. As an application we give congruences for the Klingen-Eisenstein series and cusp forms, which can be regarded as a generalization of Ramanujan's congruence. We will conclude by giving numerical examples.

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“…Here we compute the kernel of Θ : Note that b k gives the Sturm bound for M k (Γ 2 ) p (cf. [10,18]). We take a basis B = {F 1 , .…”

Section: More Examples Of Filtrationsmentioning

confidence: 99%

Weights of the Mod p Kernels of Theta Operators

2018

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We give some relations between the weights and the prime p of elements of the mod p kernel of the generalized theta operator Θ [j] . In order to construct examples of the mod p kernel of Θ [j] from any modular form, we introduce new operators A (j) (M ) and show the modularity of F |A (j) (M ) when F is a modular form. Finally, we give some examples of the mod p kernel of Θ [j] and the filtrations of some of them.

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Sturm type theorem for Siegel modular forms of genus 2 modulo p

Cited by 16 publications

References 17 publications

On the computation of the determinant of vector-valued Siegel modular forms

On the computation of the determinant of vector-valued Siegel modular forms

Ramanujan type congruences for the Klingen-Eisenstein series

Weights of the Mod p Kernels of Theta Operators

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