Number Theory

    

Behavior of Non-trivial Zeros and Prime Numbers in Reimann Hypothesis

Authors: Ricardo Gil

The Riemann Hypothesis proposes a specific location (the critical line) for the non-trivial zeros of the Riemann zeta function. This paper argues that the aperiodicity observed in the distribution of these non-trivial zeros and the distribution of primes numbers is a fundamental property. A periodic zeta function would significantly alter its behavior, rendering it irrelevant to studying prime number distribution. Conversely, a periodic pattern in prime numbers or a deviation of non-trivial zeros from the critical line would disprove the Riemann Hypothesis. The observed aperiodicity in both prime number distribution and the zeta function's non-trivial zeros strengthens the case for the Hypothesis' validity. This aperiodicity suggests a deeper connection between prime numbers and the zeta function, one that wouldn't exist with a periodic structure.

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[v1] 2024-05-15 13:35:37

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