Functions and Analysis

   

Connected Prime Digit Factorial Occurrences to The Riemann Zeta Function

Authors: Parker Emmerson

This paper explores the theoretical relationship between the frequency of prime digits in factorial representations and the non-trivial zeros of the Riemann Zeta function. By defining the prime digit frequency within fac- torials and aggregating these frequencies, we propose a hypothesis where such aggregated prime digit frequencies exhibit periodic patterns that mirror the distribution of the non-trivial zeros of the Riemann Zeta func- tion. Utilizing Fourier transform analysis, we identify periodic compo- nents in the digit frequencies that may correspond to these zeros. Sta- tistical tests, including Chi-Squared and Kolmogorov-Smirnov tests, are employed to validate this connection. This study suggests that the nature of prime digit frequencies in number sequences, such as factorials, may reflect deeper mathematical structures influenced by the Riemann Zeta functions zeros.

Comments: 8 Pages.

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Submission history

[v1] 2024-08-26 02:11:24

Unique-IP document downloads: 219 times

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