Convexity of quotients of theta functions

Atul Dixit, Arindam Roy, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

Abstract

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<∞.

Original languageEnglish (US)
Pages (from-to)319-331
Number of pages13
JournalJournal of Mathematical Analysis and Applications
Volume386
Issue number1
DOIs
StatePublished - Feb 1 2012

Keywords

  • Heat equation
  • Jacobi theta function
  • Monotonicity
  • Weierstrass elliptic function

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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