The Riemann Ξ-function under repeated differentiation

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Differentiation causes the small gaps between zeros of a given real entire function with order 1 to become larger and the larger gaps to become smaller. In this article, we show that for the Riemann Ξ-function, there exist 〈 An 〉 and 〈 Cn 〉 with Cn → 0 such thatunder(lim, n → ∞) An Ξ(2 n) (Cn z) = cos z uniformly on compact subsets of C. With our method, one can prove the same result for the analogues of the Riemann Ξ-function from automorphic L-functions. For some other Fourier transforms, we have the similar results as the Riemann Ξ-function.

Original languageEnglish
Pages (from-to)120-131
Number of pages12
JournalJournal of Number Theory
Volume120
Issue number1
DOIs
Publication statusPublished - 2006 Sep 1

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Riemann Function
L-function
Entire Function
Fourier transform
Analogue
Subset
Zero

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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The Riemann Ξ-function under repeated differentiation. / Ki, Haseo.

In: Journal of Number Theory, Vol. 120, No. 1, 01.09.2006, p. 120-131.

Research output: Contribution to journalArticle

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