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Some non-standard methods to perform calculations with Riemann's Zeta function Yu. V. Matiyasevich St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences |
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Abstract: The first part of the talk will be a short introduction the history of the study of Riemann's zeta function giving necessary (and, hopefully, sufficient) background for understanding the rest of the talk. The main part will be devoted to methods for calculating approximate values of the non-trivial zeros of Riemann's zeta functions, its values and values of its first derivative inside and outside the critical strip. These methods have been recently discovered by the author in the course of intensive numerical calculations, and so far there is no theoretical explanation of them. The obtained numerical data allows one to state a number of conjectures about the zeta function including new (so far, hypothetical) relationship between its zeros and prime numbers. More information about that ongoing research can be found at http://logic.pdmi.ras.ru/~yumat/personaljournal/artlessmethod Доклад проходит в рамках конференции “Zeta functions” http://www.mccme.ru/poncelet/2012zeta и потому будет прочитан на английском языке. Language: English |
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