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François Dress
François Dress was born August 9, 1939 in Paris. He is French national, mathematician specializing in number theory.
Early eduction at the Polytechnic School 1958 - 1960. His post graduate work; Dress received the State doctorate in mathematics in 1967 at the Faculty of Sciences of Paris, under the direction of Charles Pisot and Pierre Samuel.
His career: 1967 - 1968: lecturer at the Paris Faculty of Sciences 1968 - 2004: professor at Bordeaux 1 University
Academic Responsibilities 1987 - 1996: vice-president then provisional administrator of Bordeaux 1 University 1988 - 1992: President of CIMPA (International Center for Pure and Applied Mathematics (France - UNESCO)) in Nice
Works and publications: Analytic theory and additive number theory.
• author with Henri Cohen in 1979 of the program called Isabelle, a high-level arithmetic-oriented interpreter ancestor of PARI/gp
• (with J.-M.Deshouillers and G. Tenenbaum) Laws of distribution of divisors, 1, Acta Arithmetica, t. 34, 1979, p. 7-19 the distribution of the logarithms of the integer divisors follows on average an Arcsine law.
• (with J.-M. Deshouillers and R. Balasubramanian) Waring problem for bisquares. 1: solution diagram, C-R Acad. Sci., Paris, 303, Ser. I, 1986, p. 85-88; 2: auxiliary results for the asymptotic theorem, C-R Acad. Sci., Paris, 303, Ser. I, 1986, p. 161-163 g(4) = 19: for Waring's problem in the case of bisquares, the smallest number of bisquares necessary to express a natural number as a sum of bisquares is equal to 19.
• several articles with H. Cohen and with M. El Marraki (1993 to 2007) explicit upper bounds of the summatory functions of the Möbius function.
• Discrepancy of Farey sequences, Bordeaux Journal of Number Theory, Volume 11, No. 2, 1999, p. 345-367 the absolute discrepancy of the Farey sequence of order n is exactly 1/n.
• (with B. Landreau) Polynomials of degree greater than 2 taking many prime values, https://arxiv.org/pdf/1402.7312.pdf (2014) polynomials producing n prime numbers for n consecutive values of x, the absolute record is n = 58 found in 2010 for P(x) = (1/72) x^6 – (5/24) x^5 – (1493/72 ) x^4 + (1027/8) x^3 + (100471/18) x^2 – (11971/6) x – 57347, from x = –42 to x = 15
Honors and decorations 1968 Albert Châtelet medal 2004
Commander of the Academic Palms
References edit
Oeis:http://oeis.org/ https://oeis.org/A117081 https://oeis.org/A121887 https://oeis.org/A330363
MatheWorld: https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html
Intersections d'ensembles normaux F Dress - Journal of Number Theory, 1970 - Elsevier
Discrépance des suites de Farey F Dress - Journal de théorie des nombres de Bordeaux, 1999 - jtnb.centre-mersenne.org
Fonction sommatoire de la fonction de Möbius 1. Majorations expérimentales F Dress - Experimental Mathematics, 1993 - Taylor & Francis
Fonction sommatoire de la fonction de Mobius 2. Majorations asymptotiques élémentalres F Dress, MEI Marraki - Experimental Mathematics, 1993 - Taylor & Francis
Polynˆomes de degr´e sup´erieur `a 2 prenant beaucoup de valeurs premi`eres Fran¸cois DRESS et Bernard LANDREAU 1 7 juin 2012; https://arxiv.org/pdf/1402.7312.pdf