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We give simple numerical bounds for (s), (s), R (s), Z (t), for use in the numerical computation of these functions. The purpose of the paper is to give bounds for several functions needed in the calculation of (s) and Z (t). We are not pretending to have any originality. Our object is to be useful as a reference in our work for simple (simple to compute and simple to check) bounds.
Juan Arias de Reyna (Tue,) studied this question.