Using step functions and Poisson summation, the paper shows how the Ramanujan constant -1/12 and related zeta values emerge in Landau diamagnetism and the Casimir effect.
Shoenberg, Magnetic oscillations in metals , Cambridge University Press (1984)
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Ramanujan, Landau and Casimir, divergent series: a physicist point of view
Using step functions and Poisson summation, the paper shows how the Ramanujan constant -1/12 and related zeta values emerge in Landau diamagnetism and the Casimir effect.