We consider the -ary digital expansion of the first terms of an exponential sequence . Using a result due to Kiss and Tichy [8], we prove that the average number of occurrences of an arbitrary digital block in the last digits is asymptotically equal to the expected value. Under stronger assumptions we get a similar result for the first digits, where is a positive constant. In both methods, we use estimations of exponential sums and the concept of discrepancy of real sequences modulo plays an important role.
On s’intéresse au développement en base des premiers termes de la suite exponentielle . En utilisant un résultat dû à Kiss et Tichy, nous montrons que le nombre moyen d’occurrences d’un bloc de chiffres donné est égal asymptotiquement à sa valeur supposée. Sous une hypothèse plus forte nous montrons un résultat similaire en ne considérant seulement les , avec , premiers termes de la suite .
@article{JTNB_2002__14_2_477_0, author = {Michael Fuchs}, title = {Digital expansion of exponential sequences}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {477--487}, publisher = {Universit\'e Bordeaux I}, volume = {14}, number = {2}, year = {2002}, zbl = {1072.11006}, mrnumber = {2040688}, language = {en}, url = {https://jtnb.centre-mersenne.org/item/JTNB_2002__14_2_477_0/} }
TY - JOUR AU - Michael Fuchs TI - Digital expansion of exponential sequences JO - Journal de théorie des nombres de Bordeaux PY - 2002 SP - 477 EP - 487 VL - 14 IS - 2 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/item/JTNB_2002__14_2_477_0/ LA - en ID - JTNB_2002__14_2_477_0 ER -
Michael Fuchs. Digital expansion of exponential sequences. Journal de théorie des nombres de Bordeaux, Volume 14 (2002) no. 2, pp. 477-487. https://jtnb.centre-mersenne.org/item/JTNB_2002__14_2_477_0/
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