(x) -> x/log x
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De la Vallée Poussin is best known for his proof of the prime number theorem and his major work Cours d'analyse .
Vallée Poussin's father was the professor of geology at the University of Louvain but at first Vallée Poussin thought he would become a Jesuit. He entered the Jesuit college at Mons but he found the teaching there unacceptable and left. After this he turned to engineering and obtained his diploma in that subject. However soon after this he became attracted to pure mathematics.
In 1891 Vallée Poussin was made an assistant at the University of Louvain. He worked with Louis Claude Gilbert who had been one of his teachers. However Gilbert died in 1892 at the age of 26 and Vallée Poussin was elected to Gilbert's chair in 1893.
Vallée Poussin was elected to the Belgium Academy in 1909. More honours were to follow. There were celebrations in 1928 when Vallée Poussin had held the chair for 35 years and again celebrations in 1943 when he had been 50 years in the chair of mathematics at Louvain.
One of Vallée Poussin's first papers in 1892 on differential equations had been awarded a prize. His best known work, however, was in 1896 when he proved the prime number theorem:-
(x) -> x/log x
The prime number theorem was proved independently by Hadamard in the same year with a very different proof.
Vallée Poussin continued to work in this area publishing papers on the Riemann zeta function in 1916. Vallée Poussin also worked on approximation to functions by algebraic and trigonometric polynomials from 1908 to 1918.
Vallée Poussin's most major work was Cours d'analyse . It went through several editions, each containing new material. The third edition of Volume 2 was burned by the German army when it overran Louvain. It would have discussed the Lebesgue integral, work which was never to be published. Unlike many similar books of its time Cours d'analyse contains no complex function theory.
After 1925 Vallée Poussin turned to complex variable, potential theory and conformal representation. However publication of his work Le potential logarithmique was held up by the war and only published in 1949.
References elsewhere in this archive:
Tell me about Vallée Poussin's part in investigating prime numbers
Tell me about the Prime Number Theorem
References:
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