On an extremal problem of Selberg |
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| Authors: | Jyoichi Kaneko |
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| Institution: | aDepartment of Mathematical Sciences, University of the Ryukyus, Nishihara, Okinawa 903-0213, Japan |
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| Abstract: | We consider the minimum value mp of the product  under the conditions that  and  . This problem stems from estimation of the Selberg integral appeared in the study of integral-valued entire functions A. Selberg, Über einen Satz von A. Gelfond, Arch. Math. Naturvid. 44 (1941) 159–170]. We give upper and lower estimates of mp :  . This, in particular, slightly improves the earlier lower estimate given by Selberg: logmp>p·0.31654924…. |
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| Keywords: | Integer-valued entire function Selberg integral Electrostatic interpretation Jacobi polynomial |
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