Computation of class numbers by an analytic method
The author develops an analytic method for the computation of the class number h of an algebraic number field F. Using the functional equation of the Dedekind zeta-function he obtains h up to a factor containing R (the regulator of F) as a series expansion. The m-th term of that series involves the number of integral ideals of F of norm m and an integral over a vertical line \(Re(s)>0\). Clearly, it suffices to evaluate the series up to \(m\leq N\) for suitable N so that the remaining part is less than 1/2. The author shows that this can be done effectively. He presents a few impressive examples. Unfortunately the paper does not contain an error analysis so that the described methods will be difficult to be used by other people.
scientific article; zbMATH DE number 4027608
scientific article