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Herein we develop connections between zeta functions and some recent "mysterious" constants of nonlinear physics. In an important analysis of coupled Winfree oscillators, Quinn, Rand, and Strogatz  developed a certain N -oscillator scenario whose bifurcation phase offset φ is implicitly defined, with a conjectured asymptotic behavior: sin φ ∼ 1 − c 1 /N , with experimental estimate c 1 = 0.605443657 . . .. We are able to derive the exact theoretical value of this "QRS constant" c 1 as adoi:10.1080/10586458.2009.10128885 fatcat:unxmwm2jyjcpbdgr24q5iym3ta