Cramér’s Model for Random Primes

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Ghiasi, Mohammad | 2016

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 48700 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Alishahi, Kasra
Abstract:
With Cramer’s model we have a probability measure on the power set of N. This probability measure is concentrated on the set that its elements are that subsets of N which number of their elements up to a certain natural number is asymptotically equal with the number of primes up to the same number. Let Pc be a sample obtained from this probability measure and consider 8n 2 N, an counts the number of ways that ncan be represented as a multiplication of some elements of Pc, such that changing the arrangement of factors in a representation does not introduce a new one. In this thesis, we prove that limn!1 a1++an n almost surely exists and is positive
Keywords:
Analytic Number Theory ; Cramer's Random Model ; Stochastic Zeta Function ; Wiener-Ikehara-Tauberian Theorem