Pick's Theorem via Minkowski's Theorem

M. Ram Murty, Nithum Thain
2007 The American mathematical monthly  
Remark. Admittedly, these two suggestions for evaluating the infinite series might, for some readers, not qualify as proof. For the sceptical reader we recommend the exercise of evaluating the infinite series as a partial fraction expansion. In fact, by analogy with the elementary, real analysis derivation of ∞ k=−∞ 1/(k π + x) 2 = 1/ sin 2 x presented in [3, p. 198], we get ∞ k=−∞ 2 + (k π + x) 2 ←
doi:10.1080/00029890.2007.11920465 fatcat:ikey2zh7ufgntkrwrc22yffdie