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math.NT2026
Regularized products of Gauss and Eisenstein integers and primes
P. L. Krapivsky, J. M. Luck
We provide heuristic computations à la Euler of the regularized infinite products of Gauss and Eisenstein integers and primes. Our approach, yielding explicit expressions, is inspi…
math.NT2026
Zeta-regularization and natural boundaries: Sums and products of integers and primes
P. L. Krapivsky, J. M. Luck
Euler regularized the divergent product of all natural numbers and found beautiful formulas for regularized sums of integer powers of natural numbers. These derivations essentially…