I have used the Riemann zeta function a few times in practical option valuation, discrete barrier adjustments, Glasserman style (see for example my Incomplete Guide) or the Glass paper:
http://citeseerx.ist.psu.edu/viewdoc/do ... 1&type=pdf
see also https://www.sciencedirect.com/science/a ... 2712002567
http://www.columbia.edu/~sk75/sinica.pdf
much other use off the Riemann zeta function in finance?
Riemann Zeta Function and the Brownian Motion of Asset Prices: Number Theory meets Quantitative Finance