For fixed u and v such that 0≪u<v<1/2, the monotonicity of the quotients of Jacobi theta functions, namely, θj(u|iπt)/θj(v|iπt), j=1,2,3,4, on 0<t<∞ has been established in the previous works of A.Yu. Solynin, K. Schiefermayr, and Solynin and the first author. In the present paper, we show that the quotients θ2(u|iπt)/θ2(v|iπt) and θ3(u|iπt)/θ3(v|iπt) are convex on 0<t<∞.
- Heat equation
- Jacobi theta function
- Weierstrass elliptic function
ASJC Scopus subject areas
- Applied Mathematics