FOURIER COEFFICIENTS OF HALF-INTEGRAL WEIGHT MODULAR FORMS MODULO
FOURIER COEFFICIENTS OF HALF-INTEGRAL WEIGHT MODULAR FORMS MODULO
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半积分模形式的傅立叶系数模
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
C. Skinner
中科院分区：
文献类型：
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作者：
K. Ono;C. Skinner
S. Chowla 猜想每个素数 p 都具有这样的性质：存在无限多个类数不是 p 的倍数的虚二次域。高斯的属论保证了当 p = 2 时存在无限多个这样的域，而 Davenport 和 Heilbronn [D-H] 的工作足以满足素数 p = 3。此外，DavenportHeilbronn 的结果表明，正比例的此类域具有此性质。 Hartung [Ha] 使用基于克罗内克递推关系的基本论证证明，对于任何奇素数 p 确实存在无限多个这样的域，其类数不是 p 的倍数。他的论点已被其他类似的研究采用[Ho1，Ho2，Ho-On]。很容易捕捉到克罗内克关系的特点：如果 r(n) 将正整数 n 表示为三个平方和的表示形式的数量，则
S. Chowla conjectured that every prime p has the property that there are infinitely many imaginary quadratic fields whose class number is not a multiple of p. Gauss’ genus theory guarantees the existence of infinitely many such fields when p = 2, and the work of Davenport and Heilbronn [D-H] suffices for the prime p = 3. In addition, the DavenportHeilbronn result demonstrates that a positive proportion of such fields have this property. Using an elementary argument based on the Kronecker recurrence relations, Hartung [Ha] proved that for any odd prime p there are indeed infinitely many such fields whose class numbers are not multiples of p. His argument has been employed in other similar studies [Ho1,Ho2, Ho-On]. It is easy to capture the flavor of the Kronecker relations: if r(n) denotes the number of representations of a positive integer n as a sum of three squares, then