The Riemann hypothesis and its implications
Lecturer in science Government polytechnic, chamarajanagar-571313, Karnataka, India.
Review Article
World Journal of Advanced Research and Reviews, 2021, 10(03), 493-498
Publication history:
Received on 01 June 2021; Revised 08 June 2021; accepted on 14 June 2021
Abstract:
The Riemann Hypothesis, one of the most significant unsolved problems in mathematics, posits that all non-trivial zeros of the Riemann zeta function have a real part equal to 1/2. This paper examines the formulation of the hypothesis, its historical context, attempts at proof, and its profound implications across various mathematical domains. We explore connections to prime number distribution, quantum mechanics, and cryptography, highlighting why the hypothesis remains central to modern mathematics. While a proof remains elusive, understanding the hypothesis and its consequences provides crucial insights into the structure of numbers and the interconnected nature of mathematical fields.
Keywords:
Riemann zeta function; Prime number distribution; Analytic number theory; Critical line; Non-trivial zeros
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