Tanguy Rivoal

Rivoal obtained his Ph.D. from the Université de Caen Normandie in 2001 under the supervision of Francesco Amoroso. His dissertation was titled Propriétés diophantiennes de la fonction zêta de Riemann aux entiers impairs (Diophantine properties of the Riemann zeta function at odd integers).{{Cite thesis|url=https://theses.hal.science/tel-00004519|title = HAL these - Propriétés diophantiennes de la fonction zêta de Riemann aux entiers impairs| date=29 June 2001 | publisher=Université de Caen | last1=Rivoal | first1=Tanguy }}

Rivoal's research focuses on several areas of mathematics, including Diophantine approximation, Padé approximation, arithmetic Gevrey series, values of the Gamma function, transcendental number theory, and E-function. His notable contributions include the proof that there is at least one irrational number among nine numbers ζ(5), ζ(7), ζ(9), ζ(11), ..., ζ(21), where ζ is the Riemann zeta function.{{cite journal |author=T. Rivoal |title=Irrationalité d'au moins un des neuf nombres ζ(5), ζ(7),…, ζ(21) |journal=Acta Arithmetica |year=2002 |volume=103 |issue=2 |pages=157–167 |doi=10.4064/aa103-2-5 |url=https://eudml.org/doc/277990|arxiv=math/0104221 }}

Together with Keith Ball, Rivoal proved that an infinite number of values of ζ at odd integers are linearly independent over {{tmath|\Q}}, for which he was elected an Honorary Fellow of the Hardy-Ramanujan Society.{{cite journal |author1=K. Ball |author2=T. Rivoal |title=Irrationalité d'une infinité de valeurs de la fonction zêta aux entiers impairs |url=https://rdcu.be/d1Vol |journal=Inventiones Mathematicae |year=2001 |volume=146 |issue=1 |pages=193–207 |doi=10.1007/s002220100168|bibcode=2001InMat.146..193B }}{{Cite web|url=https://hrj.episciences.org/public/volumes/34/23Announcements.pdf|title = Announcements - Hardy-Ramanujan Journal}} They also proved that there exists an odd number j such that 1, ζ(3), and ζ(j) are linear independent over {{tmath|\Q}} where 2 < j < 170, a specific case of the more general folklore conjecture stating that {{pi}}, ζ(3), ζ(5), ζ(7), ζ(9), ..., are algebraically independent over {{tmath|\Q}}, which is a consequence of Grothendieck's period conjecture for mixed Tate motives.{{cite journal |author1=Stéphane Fischler |author2=Johannes Sprang |author3=Wadim Zudilin |title=Many odd zeta values are irrational |journal=Compositio Mathematica |year=2019 |volume=155 |issue=5 |pages=938–952 |doi=10.1112/S0010437X1900722X |url=https://www.cambridge.org/core/journals/compositio-mathematica/article/many-odd-zeta-values-are-irrational/3F6B80B30009E47D75716A96E618779D|arxiv=1803.08905 }}{{cite journal |author1=Jean-Benoît Bost |author2=François Charles |title=Some remarks concerning the Grothendieck period conjecture |journal=Journal für die reine und angewandte Mathematik |year=2016 |volume=2016 |issue=714 |pages=175–208 |doi=10.1515/crelle-2014-0025 |url=https://www.math.ens.psl.eu/~charles/crelle-periods.pdf}}{{cite journal |author=Joseph Ayoub |title=Periods and the conjectures of Grothendieck and Kontsevich-Zagier |journal=European Mathematical Society Newsletter |year=2014 |issue=91 |pages=12–18 |url=https://www.ems-ph.org/journals/newsletter/pdf/2014-03-91.pdf}}

• Apéry's constant
• Apéry's theorem
• Particular values of the Riemann zeta function
• Wadim Zudilin

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• [https://rivoal.perso.math.cnrs.fr/ Tanguy Rivoal's homepage]
• [https://rivoal.perso.math.cnrs.fr/articles.html Tanguy Rivoal's list of published works]
• {{MathGenealogy|id=64255}}

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Category:French mathematicians

Category:Number theorists

Category:Living people