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arXiv · 1502.04971

The class number formula for imaginary quadratic fields

Joseph Lewittes
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Abstract

It is shown that the class number for negative discriminant $D$ can be expressed in terms of the base $B$ expansions of reduced fractions $\frac{x}{|D|}$, where $B$ is an integer prime to $D$. This result is then formulated to obtain information about the distribution of the values of $\chi(x)$, where $\chi$ is the quadratic character associated to $D$. This leads to simplified formulas for the class number in certain cases.

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Joseph Lewittes. 2015-02-17. The class number formula for imaginary quadratic fields. https://arxiv.org/abs/1502.04971

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