In 1989, E. Saias established an asymptotic formula for with a very good error term, valid for , , We extend this result to an algebraic number field by obtaining an asymptotic formula for the analogous function with the same error term and valid in the same region. Our main objective is to compare the formulae for and and in particular to compare the second term in the two expansions.
En 1989, E. Saias a établi une formule asymptotique pour avec un très bon terme d’erreur, valable si , , Nous étendons ce résultat à un corps de nombre en obtenant une formule asymptotique pour la fonction analogue avec le même terme d’erreur et la même zone de validité. Notre objectif principal est de comparer les formules pour et en particulier comparer le second terme des développements.
@article{JTNB_2004__16_3_733_0, author = {Scourfield, Eira J.}, title = {On ideals free of large prime factors}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {733--772}, publisher = {Universit\'e Bordeaux 1}, volume = {16}, number = {3}, year = {2004}, doi = {10.5802/jtnb.468}, zbl = {1073.11061}, mrnumber = {2144965}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jtnb.468/} }
TY - JOUR AU - Scourfield, Eira J. TI - On ideals free of large prime factors JO - Journal de théorie des nombres de Bordeaux PY - 2004 SP - 733 EP - 772 VL - 16 IS - 3 PB - Université Bordeaux 1 UR - http://archive.numdam.org/articles/10.5802/jtnb.468/ DO - 10.5802/jtnb.468 LA - en ID - JTNB_2004__16_3_733_0 ER -
Scourfield, Eira J. On ideals free of large prime factors. Journal de théorie des nombres de Bordeaux, Volume 16 (2004) no. 3, pp. 733-772. doi : 10.5802/jtnb.468. http://archive.numdam.org/articles/10.5802/jtnb.468/
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