The existence of certain infinite families of imaginary quadratic fields.
The existence of certain infinite families of imaginary quadratic fields.
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某些虚二次场的无限族的存在。
DOI：
10.1515/crll.1988.390.97
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发表时间：
1988
期刊：
影响因子：
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通讯作者：
K. Horie
中科院分区：
文献类型：
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作者：
Y. Ônishi;K. Horie
Härtung[8]用二次型的Kronecker类数关系证明了存在无穷多个类数从素数到p的虚二次域。为了证明L定理，我们不仅要用Kronecker的类数关系，而且还要用Eichler[6]和Yamuchi[16]的一些迹公式，并结合某些模曲线的雅可比变种上的p-adadGalois表示(对于=-L，见[9])。类似于L定理证明的论证，再加上解析数论中的结果，得到以下结果。
Härtung [8] has proved, using Kronecker's class number relation for quadratic forms, that there exist infinitely many imaginary quadratic fields with class number prime to p. To prove Theorem l we shall use not only Kronecker's class number relation but also some trace formulae of Eichler [6] and of Yamauchi [16], combined with the p-adic Galois representations attached to the Jacobian varieties of certain modular curves (for the case = — l, see [9]). An argument similar to that of the proof of Theorem l, together with results in analytic number theory, yields the following results.