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https://www.ias.ac.in/article/fulltext/pmsc/124/04/0471-0479

Irrational factor function; races; Dirichlet 𝐿-functions.

We investigate the behavior of the sum of the irrational factor function over arithmetic progressions. We first establish a general asymptotic formula for such a sum, and then obtain some further results in the case of arithmetic progressions $3n\pm 1$.

Sneha Chaubey¹ Milenda Lanius¹ Alexandru Zaharescu¹

1. Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA.

Published

November 2014

Manuscript received

19 August 2013

Manuscript revised

17 October 2013