The Ramanujan Journal

, Volume 11, Issue 1, pp 95–102 | Cite as

Borwein's conjecture on average over arithmetic progressions

  • Alexandru ZaharescuEmail author


We provide asymptotic formulas for sums over arithmetic progressions of coefficients of products of the form
$$ R_{p_{0},s,N}(q)=\prod_{n=1}^N\prod_{j=1}^{p_0-1} (1-q^{p_0n-j})^s, $$
where s and N are positive integers and p0 is an odd prime number. We find that the sign of these sums is consistent with Borwein's conjecture.


Partial products Sums over arithmetic progressions 


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Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbana

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