A Remark on the Lindelof Hypothesis
نویسنده
چکیده
where <£fc(X)=2w=i dk(ri)e^ +residue term. Hopefully, one could expand the k integral and estimate the resulting infinite series. This does not seem feasible, however, unless k{z) satisfies a certain approximate functional equation (AFE); see [5, p. 147] and [6, p. 42]. This is one reason why only k=l, k=2 are known. However, Bellman [2] has shown that, if the e~ in k(z) are replaced by so-called Voronoi functions, one will always get an AFE. Unfortunately, these Voronoi functions have proved too messy to be useful computationally. It would therefore be of interest to see what could be done with a method which involves much simpler functions. II. Development of the main theorem. We base our development on the series
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