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Hilbert保型形式のShimura対応とその応用
http://hdl.handle.net/10076/00019445
http://hdl.handle.net/10076/00019445e571765f-4470-4d5d-aa07-9daa633a9ec2
名前 / ファイル | ライセンス | アクション |
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2020RP0008 (553.8 kB)
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Item type | 報告書 / Research Paper(1) | |||||||||||
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公開日 | 2020-11-12 | |||||||||||
タイトル | ||||||||||||
言語 | ja | |||||||||||
タイトル | Hilbert保型形式のShimura対応とその応用 | |||||||||||
タイトル | ||||||||||||
言語 | en | |||||||||||
タイトル | Shimura lifting of Hilbert modular forms and its application | |||||||||||
言語 | ||||||||||||
言語 | jpn | |||||||||||
キーワード | ||||||||||||
主題Scheme | Other | |||||||||||
主題 | Hilbert modular form | |||||||||||
キーワード | ||||||||||||
主題Scheme | Other | |||||||||||
主題 | Shimura lifting | |||||||||||
キーワード | ||||||||||||
主題Scheme | Other | |||||||||||
主題 | quadratic form | |||||||||||
キーワード | ||||||||||||
主題Scheme | Other | |||||||||||
主題 | L function | |||||||||||
資源タイプ | ||||||||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_18ws | |||||||||||
資源タイプ | research report | |||||||||||
著者 |
露峰, 茂明
× 露峰, 茂明
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抄録 | ||||||||||||
内容記述タイプ | Abstract | |||||||||||
内容記述 | (1)レベルと重さに条件を付け,半整数の重さのHilbert保型形式の志村liftができることを示し,フーリエ係数の対応を記述した.またケータ級数の3乗もlift可能であり,応用としてルート2を含む2次体Kで整数が3つの平方数の和に書ける条件を求め,その表現数とKの総虚2次拡大体の相対類数の関係を求めた. (2)保型形式f,gのn番目のフーリエ係数をそれぞれa(n), b(n)とし,a(n), そしてb(n)の複素共役を積をn番目の係数とするディリクレ級数を考える. f,gの重さや指標が異なっていてもそのL関数が全複素平面への解析接続を示し,またその関数等式を具体的に求めた.二次形式等への応用も示した. |
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抄録 | ||||||||||||
内容記述タイプ | Abstract | |||||||||||
内容記述 | (1)It is shown that Hilbert modular forms of half integral weight have Shimura lifting, provided that the level is divisible by 16 and the weight is at least 5/2. The lifting map is described explicitly in terms of Fourier coefficients. Though the condition is not satisfied, the third power of theta series has lift. As its application, the condition that algebraic integers in the quadratic field K containing square root of 2 are the sums of three squares, is obtained. Also the class numbers of the imaginary quadratic extensions of K is ordained. (2)Let f,g be elliptic modular forms of level N, and let a(n), b(n) be their n-th Fourier coefficients respectively. Let L(s;f,g) be the Dirichlet series whose n-th coefficient is a product of a(n) and the complex conjugate of b(n). Then it is shown L(s;f,g) extends meromorphically to the whole a plane, and that it has a functional equation. Also the applications to quadratic forms are shown. |
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内容記述 | ||||||||||||
内容記述タイプ | Other | |||||||||||
内容記述 | 2016年度~2018年度科学研究費補助金(基盤研究(C))研究成果報告書 | |||||||||||
書誌情報 |
発行日 2019-05-15 |
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フォーマット | ||||||||||||
内容記述タイプ | Other | |||||||||||
内容記述 | application/pdf | |||||||||||
著者版フラグ | ||||||||||||
出版タイプ | VoR | |||||||||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||||||||
出版者 | ||||||||||||
出版者 | 三重大学 | |||||||||||
出版者(ヨミ) | ||||||||||||
ミエダイガク | ||||||||||||
科研費番号 | ||||||||||||
内容記述タイプ | Other | |||||||||||
内容記述 | 16K05056 | |||||||||||
資源タイプ(三重大) | ||||||||||||
Kaken / 科研費報告書 |