Aspects of Zeta-Function Theory in the Mathematical Works of Adolf Hurwitz

Oswald, Nicola; Steuding, Jörn

doi:10.1007/978-3-319-28203-9_20

Cited by 2 publications

(2 citation statements)

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“…For more information about Hurwitz's zeta function, we refer the reader to [3,18,1,28]. Thus, to write the right-hand side of (3) in a more elementary way, we need to find the values of ζ(s, a) for odd integers and a = 1/6, 1/3, 2/3, 5/6.…”

Section: Resultsmentioning

confidence: 99%

Maximum of exponential random variables, Hurwitz's zeta function, and the partition function

2022

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A natural problem in the context of the coupon collector's problem is the behavior of the maximum of independent geometrically distributed random variables (with distinct parameters). This question has been addressed by Brennan et al. [British J. Math. Computer Sci. 8 (2015), 330-336]. Here we provide explicit asymptotic expressions for the moments of that maximum, as well as of the maximum of exponential random variables with corresponding parameters. We also deal with the probability of each of the variables being the maximal one.The calculations lead to expressions involving Hurwitz's zeta function at certain special points. We find here explicitly the values of the function at these points. Also, the distribution function of the maximum we deal with is closely related to the generating function of the partition function. Thus, our results (and proofs) rely on classical results pertaining to the partition function.

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Section: Resultsmentioning

confidence: 99%

Maximum of exponential random variables, Hurwitz's zeta function, and the partition function

2022

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“…Proof of Theorem 2: Using the same notations as in the proof of Theorem 1, by (27) and [10, p. 150, (6.3)]…”

Section: Hurwitz's Zeta Function At Special Pointsmentioning

confidence: 99%

Maximum of Exponential Random Variables, Hurwitz's Zeta Function, and the Partition Function

Barak-Pelleg¹,

Berend²,

Kolesnik³

2020

Preprint

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A natural problem in the context of the coupon collector's problem is the behavior of the maximum of independent geometrically distributed random variables (with distinct parameters). This question has been addressed by Brennan et al. (British J. of Math. & CS. 8 (2015), 330-336). Here we provide explicit asymptotic expressions for the moments of that maximum, as well as of the maximum of exponential random variables with corresponding parameters. We also deal with the probability of each of the variables being the maximal one.The calculations lead to expressions involving Hurwitz's zeta function at certain special points. We find here explicitly the values of the function at these points. Also, the distribution function of the maximum we deal with is closely related to the generating function of the partition function. Thus, our results (and proofs) rely on classical results pertaining to the partition function.

show abstract

Aspects of Zeta-Function Theory in the Mathematical Works of Adolf Hurwitz

Cited by 2 publications

References 64 publications

Maximum of exponential random variables, Hurwitz's zeta function, and the partition function

Maximum of exponential random variables, Hurwitz's zeta function, and the partition function

Maximum of Exponential Random Variables, Hurwitz's Zeta Function, and the Partition Function

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