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Factor tables 1657–1817, with notes on the birth of number theory

Maarten Bullynck (2010)

Revue d'histoire des mathématiques

The history of the construction, organisation and publication of factor tables from 1657 to 1817, in itself a fascinating story, also touches upon many topics of general interest for the history of mathematics. The considerable labour involved in constructing and correcting these tables has pushed mathematicians and calculators to organise themselves in networks. Around 1660 J. Pell was the first to motivate others to calculate a large factor table, for which he saw many applications, from Diophantine...

Fonction sommatoire de la fonction de Möbius, 3. Majorations asymptotiques effectives fortes

M. El Marraki (1995)

Journal de théorie des nombres de Bordeaux

On établit les majorations M ( x ) 0 . 002969 x ( log x ) 1 / 2 , valable pour x 142194 , M ( x ) 0 . 6437752 x log x qui est la meilleure majoration possible en x log x valable pour tout x > 1 ( M ( 5 ) = 2 = 0 . 6437752 × 5 log 5 ) , et d’autres analogues. On montre enfin comment trouver des majorations effectives M ( x ) > c k x ( log log x ) 2 k ( log x ) k pour tout k .

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