Using integrals of squares of certain real-valued special functions to prove that the P\'olya \Xi^*(z) function, the functions K_{iz}(a), a > 0, and some other entire functions have only real zeros

zbMath1163.33007arXiv0801.2996MaRDI QIDQ3614682

George Gasper

Publication date: 9 March 2009

Full work available at URL: https://arxiv.org/abs/0801.2996

zbMATH Keywords

\(K_{iz}(a)\) functionsintegrals of squaresPólya \(\Xi^*\) functionreality of zeros of entire functions

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Other functions defined by series and integrals (33E20) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

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