Newform Dedekind sums are a class of crossed homomorphisms that arise from newform Eisenstein series. We initiate a study of the kernel of these newform Dedekind sums. Our results can be loosely described as showing that these kernels are neither "too big" nor "too small." We conclude with an observation about the Galois action on Dedekind sums that allows for significant computational efficiency in the numerical calculation of Dedekind sums.

中文翻译：

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新形式 Dedekind 和的核

Newform Dedekind sums 是一类由 newform Eisenstein 级数产生的交叉同态。我们开始研究这些新形式 Dedekind 和的内核。我们的结果可以粗略地描述为表明这些内核既不是“太大”也不是“太小”。我们以对戴德金和的伽罗瓦作用的观察作为结论，它允许在戴德金和的数值计算中具有显着的计算效率。