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 [Quinn et al. 07] developed a certain N-oscillator scenario whose bifurcation phase offset small ⍉ is implicitly defined, with a conjectured asymptotic behavior sin ⍉ ~ 1−ᴄ₁/N, with experimental estimate ᴄ₁ = 0.605443657 . . .. We are able to derive the exact theoretical value of this "QRS constant" ᴄ₁ as a real zero of a particular Hurwitz zeta function. This discovery enables, for example, the rapid resolution of c1 to extreme precision. Results and conjectures are provided in regard to higher-order terms of the sin ⍉ asymptotic, and to yet more physics constants emerging from the original QRS work.
Experimental Mathematics Vol. 18, Issue 1, p. 107-116
This is an electronic version of an article published in Experimental Mathematics Vol. 18, Issue 1, p. 107-116. Experimental Mathematics is available online at: http://www.tandfonline.com/openurl?genre=article&issn=1058-6458&volume=18&issue=1&spage=107