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Nov 20, 2009 at 19:55 comment added Tom Church Couldn't you say that sin(pi x) transforms under Z with nontrivial factor of automorphy given by j(n) = (-1)^n?
Nov 20, 2009 at 4:35 comment added Nick Salter Thanks; I was thinking of introducing them by analogy with the trigonometric functions. The only issue is that with trig functions, their "automorphy factor" is always 1 and I want a good way of motivating the particular factors that arise in modular forms. I do like the observation with sin( pi x/N).
Nov 20, 2009 at 3:09 history answered JSE CC BY-SA 2.5