Denominators of Bernoulli Polynomials

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F18%3AA1901XZ0" target="_blank" >RIV/61988987:17310/18:A1901XZ0 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1112/S0025579318000153" target="_blank" >http://dx.doi.org/10.1112/S0025579318000153</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/S0025579318000153" target="_blank" >10.1112/S0025579318000153</a>

Result language
angličtina
Original language name
Denominators of Bernoulli Polynomials
Original language description
For a positive integer n let (SIM)(n) = Pi(p sp(n)>= p) p(,) where p runs over primes and s(p)(n) is the sum of the base p digits of n. For all n we prove that (SIM)(n) is divisible by all "small" primes with at most one exception. We also show that (SIM)(n) is large and has many prime factors exceeding root n, with the largest one exceeding n(20/37). We establish Kellner's conjecture that the number of prime factors exceeding root n grows asymptotically as k root/logn for some constant tc with k = 2. Further, we compare the sizes of (SIM)(n) and (SIM)(n+1), leading to the somewhat surprising conclusion that although (SIM)(n) tends to infinity with n, the inequality (SIM)(n) > (SIM)(n+1) is more frequent than its reverse.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA17-02804S" target="_blank" >GA17-02804S: Properties of number sequences and their applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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