On instances of Fox’s integral equation connection to the Riemann zeta function

Alexander E. Patkowski

Address: 1390 Bumps River Rd., Centerville, MA 02632, USA

E-mail: alexpatk@hotmail.com

Abstract: We consider some applications of the singular integral equation of the second kind of Fox. Some new solutions to Fox’s integral equation are discussed in relation to number theory.

AMSclassification: primary 42A38; secondary 11L20.

Keywords: Fourier integrals, Fox’s integral equation, Riemann prime counting function.

DOI: 10.5817/AM2019-3-195