The Experts below are selected from a list of 48 Experts worldwide ranked by ideXlab platform
Shoyu Nagaoka - One of the best experts on this subject based on the ideXlab platform.
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Theta Operator on hermitian modular forms over the eisenstein field
Ramanujan Journal, 2020Co-Authors: Shoyu Nagaoka, Sho TakemoriAbstract:The mod p kernel of the Theta Operator on Hermitian modular forms is studied in the case that the base field is the Eisenstein field.
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on the mod p kernel of the Theta Operator and eisenstein series
Journal of Number Theory, 2018Co-Authors: Shoyu Nagaoka, Sho TakemoriAbstract:Abstract Siegel modular forms in the space of the mod p kernel of the Theta Operator are constructed by the Eisenstein series in some odd-degree cases. Additionally, a similar result in the case of Hermitian modular forms is given.
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Theta Operator for hermitian modular forms over the eisenstein field
arXiv: Number Theory, 2018Co-Authors: Shoyu Nagaoka, Sho TakemoriAbstract:In this paper, we have investigated the mod p kernel of the Theta Operator for Hermitian modular forms when the base field is the Eisenstein field.
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on the kernel of the Theta Operator mod p
Manuscripta Mathematica, 2018Co-Authors: Siegfried Bocherer, Hirotaka Kodama, Shoyu NagaokaAbstract:We construct many examples of level one Siegel modular forms in the kernel of Theta Operators mod p by using Theta series attached to positive definite quadratic forms.
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on the Theta Operator for hermitian modular forms of degree 2
Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg, 2017Co-Authors: Toshiyuki Kikuta, Shoyu NagaokaAbstract: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.
Sho Takemori - One of the best experts on this subject based on the ideXlab platform.
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Theta Operator on hermitian modular forms over the eisenstein field
Ramanujan Journal, 2020Co-Authors: Shoyu Nagaoka, Sho TakemoriAbstract:The mod p kernel of the Theta Operator on Hermitian modular forms is studied in the case that the base field is the Eisenstein field.
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on the mod p kernel of the Theta Operator and eisenstein series
Journal of Number Theory, 2018Co-Authors: Shoyu Nagaoka, Sho TakemoriAbstract:Abstract Siegel modular forms in the space of the mod p kernel of the Theta Operator are constructed by the Eisenstein series in some odd-degree cases. Additionally, a similar result in the case of Hermitian modular forms is given.
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Theta Operator for hermitian modular forms over the eisenstein field
arXiv: Number Theory, 2018Co-Authors: Shoyu Nagaoka, Sho TakemoriAbstract:In this paper, we have investigated the mod p kernel of the Theta Operator for Hermitian modular forms when the base field is the Eisenstein field.
Ian Kiming - One of the best experts on this subject based on the ideXlab platform.
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on the Theta Operator for modular forms modulo prime powers
Mathematika, 2016Co-Authors: Imin Chen, Ian KimingAbstract:We consider the classical Theta Operator θ on modular forms modulo pm and level N prime to p where p is a prime greater than 3. Our main result is that θ mod pm will map forms of weight k to forms of weight k + 2 + 2pm−1(p − 1) and that this weight is optimal in certain cases when m is at least 2. Thus, the natural expectation that θ mod pm should map to weight k + 2 + pm−1(p− 1) is shown to be false. The primary motivation for this study is that application of the θ Operator on eigenforms mod pm corresponds to twisting the attached Galois representations with the cyclotomic character. Our construction of the θ-Operator mod pm gives an explicit weight bound on the twist of a modular mod pm Galois representation by the cyclotomic character.
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on the Theta Operator for modular forms modulo prime powers
arXiv: Number Theory, 2013Co-Authors: Imin Chen, Ian KimingAbstract:We consider the classical Theta Operator $\Theta$ on modular forms modulo $p^m$ and level $N$ prime to $p$ where $p$ is a prime greater than 3. Our main result is that $\Theta$ mod $p^m$ will map forms of weight $k$ to forms of weight $k+2+2p^{m-1}(p-1)$ and that this weight is optimal in certain cases when $m$ is at least 2. Thus, the natural expectation that $\Theta$ mod $p^m$ should map to weight $k+2+p^{m-1}(p-1)$ is shown to be false. The primary motivation for this study is that application of the $\Theta$ Operator on eigenforms mod $p^m$ corresponds to twisting the attached Galois representations with the cyclotomic character. Our construction of the $\Theta$-Operator mod $p^m$ gives an explicit weight bound on the twist of a modular mod $p^m$ Galois representation by the cyclotomic character.
Eyal Z Goren - One of the best experts on this subject based on the ideXlab platform.
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a Theta Operator on picard modular forms modulo an inert prime
Research in the Mathematical Sciences, 2016Co-Authors: Ehud De Shalit, Eyal Z GorenAbstract:To thememory of Robert Coleman *Correspondence: deshalit@math.huji.ac.il 1Hebrew University, Jerusalem, Israel Full list of author information is available at the end of the article
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a Theta Operator on picard modular forms modulo an inert prime
arXiv: Number Theory, 2014Co-Authors: Ehud De Shalit, Eyal Z GorenAbstract:We study the reduction of Picard modular surfaces modulo an inert prime, mod p and p-adic modular forms. We construct a Theta Operator on such modular forms and study its poles and its effect on Fourier-Jacobi expansions.
Imin Chen - One of the best experts on this subject based on the ideXlab platform.
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on the Theta Operator for modular forms modulo prime powers
Mathematika, 2016Co-Authors: Imin Chen, Ian KimingAbstract:We consider the classical Theta Operator θ on modular forms modulo pm and level N prime to p where p is a prime greater than 3. Our main result is that θ mod pm will map forms of weight k to forms of weight k + 2 + 2pm−1(p − 1) and that this weight is optimal in certain cases when m is at least 2. Thus, the natural expectation that θ mod pm should map to weight k + 2 + pm−1(p− 1) is shown to be false. The primary motivation for this study is that application of the θ Operator on eigenforms mod pm corresponds to twisting the attached Galois representations with the cyclotomic character. Our construction of the θ-Operator mod pm gives an explicit weight bound on the twist of a modular mod pm Galois representation by the cyclotomic character.
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on the Theta Operator for modular forms modulo prime powers
arXiv: Number Theory, 2013Co-Authors: Imin Chen, Ian KimingAbstract:We consider the classical Theta Operator $\Theta$ on modular forms modulo $p^m$ and level $N$ prime to $p$ where $p$ is a prime greater than 3. Our main result is that $\Theta$ mod $p^m$ will map forms of weight $k$ to forms of weight $k+2+2p^{m-1}(p-1)$ and that this weight is optimal in certain cases when $m$ is at least 2. Thus, the natural expectation that $\Theta$ mod $p^m$ should map to weight $k+2+p^{m-1}(p-1)$ is shown to be false. The primary motivation for this study is that application of the $\Theta$ Operator on eigenforms mod $p^m$ corresponds to twisting the attached Galois representations with the cyclotomic character. Our construction of the $\Theta$-Operator mod $p^m$ gives an explicit weight bound on the twist of a modular mod $p^m$ Galois representation by the cyclotomic character.