Geodesic
Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions
Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 551-561

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DOI

For relatively prime positive integers ${{u}_{0}}$ and $r$ , we consider the least common multiple ${{L}_{n}}\,:=\,\text{lcm}\left( {{u}_{0}},\,{{u}_{1}},\,.\,.\,.\,,\,{{u}_{n}} \right)$ of the finite arithmetic progression $\left\{ {{u}_{k}}\,:=\,{{u}_{0}}\,+\,kr \right\}_{k=0}^{n}$ . We derive new lower bounds on ${{L}_{n}}$ that improve upon those obtained previously when either ${{u}_{0}}$ or $n$ is large. When $r$ is prime, our best bound is sharp up to a factor of $n\,+\,1$ for ${{u}_{0}}$ properly chosen, and is also nearly sharp as $n\,\to \,\infty$ .
DOI : 10.4153/CMB-2014-017-0
Mots-clés : 11A05, least common multiple, arithmetic progression 
Kane, Daniel M.; Kominers, Scott Duke. Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions. Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 551-561. doi: 10.4153/CMB-2014-017-0
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     author = {Kane, Daniel M. and Kominers, Scott Duke},
     title = {Asymptotic {Improvements} of {Lower} {Bounds} for the {Least} {Common} {Multiples} of {Arithmetic} {Progressions}},
     journal = {Canadian mathematical bulletin},
     pages = {551--561},
     year = {2014},
     volume = {57},
     number = {3},
     doi = {10.4153/CMB-2014-017-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-017-0/}
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