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A stochastic interpretation of the Riemann zeta function
K S Alexander1, K Baclawski, G C Rota
1Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA.
Summary
We introduce a novel stochastic process where the Riemann zeta function
Area of Science:
- Number Theory
- Probability Theory
- Stochastic Processes
Background:
- The Riemann zeta function is a complex function of profound importance in number theory.
- Understanding its properties often involves advanced analytical techniques.
- Connecting number theory concepts to probability theory remains an active area of research.
Purpose of the Study:
- To establish a novel stochastic process.
- To demonstrate that the terms of the Riemann zeta function emerge as probability distributions.
- To bridge number theoretic functions with probabilistic frameworks.
Main Methods:
- Construction of a specific stochastic process.
- Identification of elementary random variables within this process.
- Analysis of the probability distributions associated with these random variables.
Main Results:
- The probability distributions of the elementary random variables are shown to be the terms of the Riemann zeta function.
- This provides a probabilistic interpretation for the values of the Riemann zeta function.
Conclusions:
- A new stochastic framework is presented for studying the Riemann zeta function.
- This approach offers a potentially intuitive way to explore the properties of the Riemann zeta function.
- The findings open avenues for interdisciplinary research between number theory and probability.
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