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The addition formula for theta functions


In this paper we solve the functional equationx(u + v)ϕ(u − v) = f 1(u)g1(v) + f2(u)g2(v) under the assumption thatx, ϕ, f 1, f2, g1, g2 are complex-valued functions onR n,n ∈ N arbitrary, andχ ≢ 0 andϕ ≢ 0 are continuous. Our main result shows that, apart from degeneracy and some obvious modifications, theta functions of one complex variable are the only continuous solutions of this functional equation.

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Bonk, M. The addition formula for theta functions. Aeq. Math. 53, 54–72 (1997).

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AMS subject classification (1991)

  • Primary 39B32
  • Secondary 33E05