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

Mohinur Raupova; Zilola Fayziyeva

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

How to Cite

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