the regulator in physical problems, before , J. Stuart Dowker and Raymond Critchley in 1976 proposed a zeta-function regularization method for quantum physical problems. Emilio Elizalde and others have also proposed a method based on the zeta regularization for the integrals , here is a regulator and the divergent integral depends on the numbers in the limit see renormalization. Also unlike other regularizations such as dimensional regularization and analytic regularization, zeta regularization has no counterterms and gives only finite results. See also Generating function Perron's formula Renormalization 1 + 1 + 1 + 1 + ⋯ 1 + 2 + 3 + 4 + ⋯ Analytic torsion Ramanujan summation Minakshisundaram–Pleijel zeta function Zeta function (operator) References Tom M. Apostol, "Modular Functions and Dirichlet Series in Number Theory", "Springer-Verlag New York. (See Chapter 8.)" A. Bytsenko, G. Cognola, E. Elizalde, V. Moretti and S. Zerbini, "Analytic Aspects of Quantum Fields", World Scientific Publishing, 2003, G.H. Hardy and J.E. Littlewood, "Contributions to the Theory of the Riemann Zeta-Function and the Theory of the Distribution of Primes", Acta Mathematica, 41(1916) pp. 119–196. (See, for example, theorem 2.12) V. Moretti, "Direct z-function approach and renormalization of one-loop stress tensor in curved spacetimes, Phys. Rev.D 56, 7797 ''(1997). Quantum field theory String theory Mathematical analysis Zeta and L-functions Summability methods