Petersson scalar product and L-functions arising from modular forms
Petersson scalar product and L-functions arising from modular forms
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由模块化形式产生的 Petersson 标量积和 L 函数
DOI：
10.1007/s11139-019-00159-8
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发表时间：
2019
影响因子：
0.7
通讯作者：
S. Tsuyumine
中科院分区：
文献类型：
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作者：
S. Tsuyumine
设f（z）=∑n=0∞ane（nz），g（z）=∑n=0∞bne（nz）（e（z）=e2π-1z）是整权或半整权的全纯模形式，其中它们的权或特征标不一定相等.我们证明了它是全平面的亚纯延拓，并且满足一些函数方程。L-函数的某些留数或某些特殊值用Petersson标积表示。应用二次形式包括在内。
Let f(z)=∑n=0∞ane(nz),g(z)=∑n=0∞bne(nz)(e(z)=e2π-1z) be holomorphic modular forms forof integral weight or half integral weight, where their weights or characters are not necessarily equal to each other. We show thatextends meromorphically to the wholesplane, and that it satisfies some functional equation. Some residues of theL-function or some special values are expressed in terms of the Petersson scalar product. Applications to quadratic forms are included.