11 resultados para Riemann hypothesis

em Bulgarian Digital Mathematics Library at IMI-BAS


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AMS Subj. Classification: 11M41, 11M26, 11S40

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2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.

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Riemann’s memoir is devoted to the function π(x) defined as the number of prime numbers less or equal to the real and positive number x. This is really the fact, but the “main role” in it is played by the already mentioned zeta-function.

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AMS Subject Classification 2010: 11M26, 33C45, 42A38.

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We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system. It yields an explicit symplectic representation of the braid groups (coloured or not) of four strings.

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A procedure for calculating critical level and power of likelihood ratio test, based on a Monte-Carlo simulation method is proposed. General principles of software building for its realization are given. Some examples of its application are shown.

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2000 Mathematics Subject Classification: 33D60, 26A33, 33C60

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2000 Mathematics Subject Classification: 35A15, 44A15, 26A33

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Mathematics Subject Classification: 42A38, 42C40, 33D15, 33D60

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2010 Mathematics Subject Classification: 35Q15, 31A25, 37K10, 35Q58.