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Some Identities on the Character Sum Containing x(x - 1)(x - λ)

Published online by Cambridge University Press:  22 January 2016

Masatoshi Yamauchi
Masatoshi Yamauchi*
Affiliation:
Mathematical Institute, Nagoya University
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Let Fp be the prime field of characteristic p (p: an odd prime), and put = Fp - {0, 1}. Then for λ ∈ we define

,

where denotes the Legendre symbol, and consider the sum

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 42 , March 1971 , pp. 109 - 113
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

References

[1] Birch, B.J., How the number of points of elliptic curves over a fixed prime field varies, J. London Math. Soc., 43 (1968), 57–60.CrossRefGoogle Scholar
[2] Birch, B.J., Weber’s class invariants, Mathematika, 16 (1969), 283–294.CrossRefGoogle Scholar
[3] Yamauchi, M., On the trace of Hecke operators for certain modular groups, to appear.CrossRefGoogle Scholar