[1804.10043] Riemann, Thorin, van Dantzig Pairs, Wald Couples and Hadamard Factorisation Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Probability arXiv:1804.10043 (math) [Submitted on 19 Apr 2018 ( v1 ), last revised 29 Apr 2026 (this version, v8)] Title: Riemann, Thorin, van Dantzig Pairs, Wald Couples and Hadamard Factorisation Authors: Nicholas G. Polson View a PDF of the paper titled Riemann, Thorin, van Dantzig Pairs, Wald Couples and Hadamard Factorisation, by Nicholas G. Polson View PDF HTML (experimental) Abstract: Zeros of entire functions can be found using either the Fourier methods of Riemann-Polya or the Generalized Gamma Convolution (GGC) methods of Thorin-Bondesson. This connection is based on a duality between the Hadamard-Weierstrass factorisation and van Dantzig Pairs-Wald couples of random variables. We demonstrate the methodology on particular functions including the Riemann zeta and xi-functions, Ramanujan's tau function, L-functions and Gamma and Hyperbolic functions. Subjects: Probability (math.PR) Cite as: arXiv:1804.10043 [math.PR] (or arXiv:1804.10043v8 [math.PR] for this version) https://doi.org/10.48550/arXiv.1804.10043 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Nicholas Polson Prof [ view email ] [v1] Thu, 19 Apr 2018 02:50:34 UTC (14 KB) [v2] Sat, 28 Apr 2018 17:28:31 UTC (14 KB) [v3] Mon, 28 May 2018 11:47:36 UTC (15 KB) [v4] Tue, 26 Jun 2018 13:15:35 UTC (15 KB) [v5] Mon, 17 May 2021 22:32:01 UTC (16 KB) [v6] Tue, 6 Jul 2021 03:10:58 UTC (18 KB) [v7] Thu, 9 Sep 2021 15:58:46 UTC (19 KB) [v8] Wed, 29 Apr 2026 20:15:55 UTC (20 KB) Full-text links: Access Paper: View a PDF of the paper titled Riemann, Thorin, van Dantzig Pairs, Wald Couples and Hadamard Factorisation, by Nicholas G. Polson View PDF HTML (experimental) TeX Source view license Current browse context: math.PR < prev | next > new | recent | 2018-04 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from