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I'm interested in the s-derivative at s=0 of the analytic continuation of
Up to an overall gamma function and a constant, by taking the proper Mellin transform this is equal to the integral
where θ is a Jacobian theta function. Does this function have a name? (The Hurwitz zeta function initially seems promising, but doesn't quite do the trick.) I'd like to compute , provided it can be done in elementary transcendental functions. 71.182.216.55 (talk) 01:29, 22 March 2009 (UTC)
Yeah, so the question is still live, despite recent activity on earlier threads ;-) Is anyone here knowledgable about arithmetic? 71.182.216.55 (talk) 04:08, 22 March 2009 (UTC)
The problem is interesting because it is the zeta function regularization of the determinant of the Laplacian on the flat (square) torus. Despite the fact that the should be the easiest test case of the determinant, it actually appears to me to be non-trivial. (It turns out that disks in symmetric spaces are easier, provided one believes in radial functions.) 71.182.216.55 (talk) 04:43, 22 March 2009 (UTC)
I am wondering: (A) if there are any actual studies or "real" data to answer my question or, if not, (B) if anyone has any relevant ideas or theories to suggest. My question is this. Statistically speaking, is any one day of the year equally likely to be someone's birthday as any other day of the year? In other words ... does a birthday of January 1 come up with equal probability as a birthday of January 2, January 3, January 4, ... and so on ... until December 31? Perhaps stated another way ... does each day of the year actually have a probability of 1/365? (I assume that, at least theoretically, they do ... right?) Are there any data or studies about this? If not, can anyone think of any ideas / reasons / theories as to why one particular birthday might show up with greater (or lesser) frequency than another? For sake of simplicity and convenience in this question, let's ignore the birthday of February 29. Thanks. (Joseph A. Spadaro (talk) 20:15, 22 March 2009 (UTC))