On this page I've collected several useful resources related to my 2019 paper "Orthogonal polynomial expansions for the Riemann xi function" and its 2021 journal version "Orthogonal polynomial expansions for the Riemann xi function in the Hermite, Meixner-Pollaczek, and continuous Hahn bases".

Background

"Orthogonal polynomial expansions for the Riemann xi function" is a long paper I wrote in 2019. In 2021 I created a shorter version of the paper with some of the less significant results removed, which was accepted for publication in the journal Acta Mathematica. I gave the shorter version a different (longer!) title, "Orthogonal polynomial expansions for the Riemann xi function in the Hermite, Meixner-Pollaczek, and continuous Hahn bases", to allow each of the versions to be cited as distinct works. The results from the longer version that were removed from the short version are still interesting and I may submit them for publication as a separate paper in the future.

• PDF of the journal version (to appear in Acta Mathematica).
• PDF of the original, longer paper (version of May 5, 2019, updated from earlier version).

Resources

• Papers by Pál (Paul) Turán on the Hermite expansion of the Riemann xi function:

  • Sur l'algèbre fonctionnelle. Comptes Rendus du Premier Congrès des Mathématiciens Hongrois, 27 Août–2 Septembre 1950. Akadémiai Kiadó, 1952, pp. 279–290. Reprinted in Collected Papers of Paul Turán, Ed. P. Erdős, Vol. 1, pp. 677–688. Akadémiai Kiadó, 1990.

  • On functional algebra. English translation of the paper Sur l'algèbre fonctionnelle. Translated from the French by Dan Romik, with additional remarks and corrections by Jacques Gélinas, March 2019.

  • Hermite-expansion and strips for zeros of polynomials. Arch. Math. 5 (1954), 148–152. Reprinted in Collected Papers of Paul Turán, Ed. P. Erdős, Vol. 1, pp. 738–742. Akadémiai Kiadó, 1990.

  • To the analytical theory of algebraic equations. Bulgar. Akad. Nauk. Otd. Mat. Fiz. Nauk. Izv. Mat. Inst. 3 (1959), 123–137. Reprinted in Collected Papers of Paul Turán, Ed. P. Erdős, Vol. 2, pp. 1080–1090. Akadémiai Kiadó, 1990.

• List of versions of the long paper and log of changes: (all versions can be found on the paper's arXiv page)
  • Version 1: Feb. 17, 2019
  • Version 2: Mar. 5, 2019. Changes from previous version: Minor edits to improve presentation and correct typos. Added a remark following Theorem 4.16. Added a citation to a 2018 paper by Griffin, Ono, Rolen and Zagier, and a brief discussion on pages 82-83 comparing my paper's Theorem 6.1 to Theorem 7 in Griffin et al's paper.
  • Version 3: May 5, 2019. Changes from previous version: Typo corrections. Edits to Chapter 4 adding references and clarifying remarks. Moved Proposition 6.2 from Chapter 6 to Section 4.8. Replaced proof of Proposition 4.18 (formerly Proposition 4.17) with a simpler one.
• List of changes between the long paper and the short paper:
  • Chapter 4 has been removed in the short paper.
  • Appendix B has been removed in the short paper, and Appendix A shortened.
  • The abstract and parts of the introduction were rewritten in the short paper.
  • Other minor formatting and cosmetic adjustments.