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Spectral functions, such as the zeta functions, are widely used in QuantumField Theory to calculate physical quantities. In this work, we compute theelectrostatic potential and field due to an infinite discrete distribution ofpoint charges, using the zeta function regularization technique. This methodallows us to remove the infinities that appear in the resulting expression. Wefound that the asymptotic behavior dependence of the potential and field issimilar to the cases of continuous charge distribution. Finally, this exercisecan be useful for graduate students to explore spectral and special functions.

Zeta function regularization technique in the electrostatics context for discrete charge distributions