Convexity of quotients of theta functions

Atul Dixit; Arindam Roy; Alexandru Zaharescu

doi:10.1016/j.jmaa.2011.08.012

Convexity of quotients of theta functions

Atul Dixit, Arindam Roy, Alexandru Zaharescu

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

For fixed u and v such that 0≪u<v<1/2, the monotonicity of the quotients of Jacobi theta functions, namely, θ_j(u|iπt)/θ_j(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 language	English (US)
Pages (from-to)	319-331
Number of pages	13
Journal	Journal of Mathematical Analysis and Applications
Volume	386
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2011.08.012
State	Published - Feb 1 2012

Keywords

Heat equation
Jacobi theta function
Monotonicity
Weierstrass elliptic function

ASJC Scopus subject areas

Analysis
Applied Mathematics

Online availability

10.1016/j.jmaa.2011.08.012

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title = "Convexity of quotients of theta functions",

keywords = "Heat equation, Jacobi theta function, Monotonicity, Weierstrass elliptic function",

author = "Atul Dixit and Arindam Roy and Alexandru Zaharescu",

note = "Funding Information: E-mail addresses: [email protected] (A. Dixit), [email protected] (A. Roy), [email protected] (A. Zaharescu). 1 The author is supported by NSF grant number DMS-0901621.",

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T1 - Convexity of quotients of theta functions

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AU - Roy, Arindam

AU - Zaharescu, Alexandru

N1 - Funding Information: E-mail addresses: [email protected] (A. Dixit), [email protected] (A. Roy), [email protected] (A. Zaharescu). 1 The author is supported by NSF grant number DMS-0901621.

PY - 2012/2/1

Y1 - 2012/2/1

KW - Heat equation

KW - Jacobi theta function

KW - Monotonicity

KW - Weierstrass elliptic function

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DO - 10.1016/j.jmaa.2011.08.012

M3 - Article

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Convexity of quotients of theta functions

Abstract

Keywords

ASJC Scopus subject areas

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