Number Theory

    

Spectral Analysis of Arithmetic Functions

Authors: George Athanasiou

This paper explores the normalization of Fourier series kernelsassociated with elementary arithmetic functions. By analyzing keyfunctions such as divisor related functions, the prime gap function andthe inverse prime counting function. With these results, a framework fortheir spectral decomposition in terms of complex exponential functionswas developed. Through contour integration techniques and normalizationof the Dirac delta function, new methods can be derived from the analyticstructure of these functions. These findings contribute to the broaderunderstanding of arithmetic functions and their link to Fourier series.

Comments: 9 Pages.

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[v1] 2026-07-29 14:47:14

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