Computational Methods and Function Theory 4 (2004), No. 1, 143--150
Copyright Heldermann Verlag 2004
Paul M. Gauthier
gauthier@dms.umontreal.ca , Dépt. Mathématiques et Statistique, Université de Montréal, Centreville, Montréal, QC, H3C 3J7, Canada.
Eduardo S. Zeron
eszeron@math.cinvestav.mx , Depto. Matemáticas, Civestav, Apdo. Postal 14-740, México DF, 07000, México.
It is shown that the Riemann hypotheses fails for two types of arbitrarily close approximations of the Riemann zeta function. The first type is meromorphic and approximates the zeta function outside of a small set. The second type is quasi-meromorphic, agrees with the zeta function outside of an even smaller set and approximates the zeta function everywhere.
Keywords: Tangential approximation, Riemann zeta function.
MSC 2000: 11M26, 30C62, 30E10.
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