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  • Canadian Mathematical Bulletin

Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions

By: Daniel M. Kane and Scott Duke Kominers
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Abstract

For relatively prime positive integers and r, we consider the least common multiple L_n:=\mathop{\textrm{lcm}}(u_0,u_1,\dots, u_n) of the finite arithmetic progression \{u_k:=u_0+kr\}_{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.

Keywords

Mathematical Methods

Citation

Kane, Daniel M., and Scott Duke Kominers. "Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions." Canadian Mathematical Bulletin 57, no. 3 (September 2014): 551–561.

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Scott Duke Kominers

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