| A note on Weil index |
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| 作者姓名： | Jing-song CHAI Xu-ri CONG Center of Mathematical Sciences Zhejiang University Hangzhou China |
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| 作者单位： | Jing-song CHAI Xu-ri CONG Center of Mathematical Sciences，Zhejiang University，Hangzhou 310027，China |
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| 基金项目： | The authors would like to thank their advisor Prof. Li Jian-shu for his suggestion and his constant encouragement. |
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| 摘 要： | Let F be a non-archimedean local field of characteristic 0 and(?)a nontrivial additive character.Weil first defined the Weil indexγ(a,(?))(a∈F~*)in his famous paper,from which we know thatγ(a,(?))γ(b,(?))=γ(ab,(?))γ(1,(?))(a,b)andγ(a,(?))~4 =(-1,-1),where(a,b)is the Hilbert symbol for F.The Weil index plays an important role in the theory of theta series and in the general representation theory.In this paper,we establish an identity relating the Weil indexγ(a,(?))and the Gauss sum.
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| 收稿时间： | 19 November 2006 |
| 修稿时间： | 12 December 2006 |
A note on Weil index |
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| Jing-song CHAI Xu-ri CONG Center of Mathematical Sciences,Zhejiang University,Hangzhou ,China.A note on Weil index[J].Science in China(Mathematics),2007,50(7):951-956. |
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| Authors: | Jing-song Chai Xu-ri Cong |
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| Institution: | Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China |
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| Abstract: | Let F be a non-archimedean local field of characteristic 0 and ψ a nontrivial additive character. Weil first defined the Weil index γ(a, ψ) (a ∊ F*) in his famous paper, from which we know that γ(a, ψ)γ(b, ψ) = γ(ab, ψ)γ(1, ψ)(a, b) and γ(a, ψ)4 = (−1, −1), where (a, b) is the Hilbert symbol for F. The Weil index plays an important role in the theory of theta series and in the general representation theory. In this paper,
we establish an identity relating the Weil index γ(a, ψ) and the Gauss sum.
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| Keywords: | Weil index Hilbert symbol local fields Gauss sum |
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