J. Hadamard, Sur la distribution des zeros de la fonction #(s) et ses consequences arithmetiques, Bull. Soc. Math. de France, 24, 1896, p.199-220. Home/Search Document Not in Database Summary Related Articles |
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On the Number of Prime Numbers less than a Given Quantity - Kolev (2000) (Correct)
....line #z = 1 2 . This conjecture is one of the most celebrated open problems in all of mathematics. 5 The first proofs of the prime number theorem were given independently in 1896 by Jacques Salomon Hadamar (1865 1963) and Charles Jean Gustave Nicolas de la Vallee Poussin (1866 1962) in [13, 28]) Although they di#er in details both proofs follow Riemann ideas and establish the existence of a zero free region for #(z) in the critical strip. Precisely, the following asymptotic was proved: #(x) Li(x) O(x e a # log x ) 10) where a is some positive constant. In the same paper de la ....
J. Hadamard, Sur la distribution des zeros de la fonction #(s) et ses consequences arithmetiques, Bull. Soc. Math. de France, 24, 1896, p.199-220.
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