PRIME NUMBERS, ZETA FUNCTIONS, AND THE RIEMANN HYPOTHESIS: A COMPREHENSIVE REVIEW

Authors

  • Mohinur Raupova Chirchiq State Pedagogical University
  • Zilola Fayziyeva 3rd Year Student, Chirchiq State Pedagogical University

Keywords:

Prime numbers, Riemann zeta function, Riemann Hypothesis, number theory, critical strip, prime counting function, zero distribution, analytical methods.

Abstract

This comprehensive review examines the intricate relationship between prime numbers, the Riemann zeta function, and the celebrated Riemann Hypothesis. We analyze historical developments, current theoretical frameworks, and computational approaches in understanding prime number distribution. The study synthesizes classical results with modern computational methods, providing insights into one of mathematics' most profound unsolved problems. Special attention is given to recent algorithmic approaches and numerical verifications of the hypothesis up to significant heights on the critical line.

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Published

2025-01-17

Issue

Section

Articles

How to Cite

PRIME NUMBERS, ZETA FUNCTIONS, AND THE RIEMANN HYPOTHESIS: A COMPREHENSIVE REVIEW. (2025). Web of Technology: Multidimensional Research Journal, 3(1), 53-56. https://webofjournals.com/index.php/4/article/view/2896