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Hermanus Johannes Joseph te Riele (born 5 January 1947) is a Dutch mathematician at CWI in Amsterdam with a specialization in computational number theory. He is known for proving the correctness of the Riemann hypothesis for the first 1.5 billion non-trivial zeros of the Riemann zeta function with Jan van de Lune and Dik Winter, for disproving the Mertens conjecture with Andrew Odlyzko, and for factoring large numbers of world record size. In 1987, he found a new upper bound for π(x) − Li(x).
In 1970, Te Riele received an engineer's degree in mathematical engineering from Delft University of Technology and, in 1976, a PhD degree in mathematics and physics from University of Amsterdam (1976).
- "Disproof of the Mertens conjecture". Journal für die reine und angewandte Mathematik (Crelle's Journal). 1985 (357). Walter de Gruyter GmbH: 138–160. 1 March 1985. doi:10.1515/crll.1985.357.138. ISSN 0075-4102. S2CID 13016831.
- Brent, R. P.; van de Lune, J.; te Riele, H. J. J.; Winter, D. T. (1982). "On the zeros of the Riemann zeta function in the critical strip. II". Mathematics of Computation. 39 (160). American Mathematical Society (AMS): 681–688. doi:10.1090/s0025-5718-1982-0669660-1. ISSN 0025-5718.
- te Riele, Herman J. J. (1987). "On the sign of the difference 𝜋(𝑥)-𝑙𝑖(𝑥)". Mathematics of Computation. 48 (177). American Mathematical Society (AMS): 323–328. doi:10.1090/s0025-5718-1987-0866118-6. ISSN 0025-5718.
- Kleinjung, Thorsten; Aoki, Kazumaro; Franke, Jens; Lenstra, Arjen K.; Thomé, Emmanuel; Bos, Joppe W.; Gaudry, Pierrick; Kruppa, Alexander; Montgomery, Peter L.; Osvik, Dag Arne; te Riele, Herman; Timofeev, Andrey; Zimmermann, Paul (2010). "Factorization of a 768-Bit RSA Modulus". Advances in Cryptology – CRYPTO 2010. Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-642-14623-7_18. ISBN 978-3-642-14622-0. ISSN 0302-9743. S2CID 11556080.
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