Mathematical Sciences: "The Convergence of Euler Products"

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The matrix generalization of the Euler product has been introduced in previous work, and it has been shown that the Riemann Hypothesis is equivalent to the convergence question for related products of Moebius transformations. The present project is an estimation theory of such products which would be sufficient to answer the question posed by Riemann. In order to accomplish this it is proposed to construct disks that are mapped into each other by successive Moebius transformations of the matrix product. The solution of the Riemann Hypothesis is indeed the Holy Grail of analysis, and the principal investigator is by most accounts the most capable person in the world to attempt a solution. Even if a complete resolution does not result from this work the results that are obtained will be of tremendous value.