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Borwein's conjecture on average over arithmetic progressions

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Abstract

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.

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References

  1. Andrews, G.E.: On an conjecture of Peter Borwein, Symbolic computation in combinatorics Δ1 (Ithaca, NY, 1993). J. Symbolic Comput. 20(5/6), 487–501 (1995)

    Google Scholar 

  2. Andrews, G.E., Baxter, R.J., Bressoud, D.M., Burge, W.H., Forrester, P.J., Viennot, G.: Partitions with prescribed hook differences. European J. Combin. 8(4), 341–350 (1987)

    MathSciNet  Google Scholar 

  3. Bailey, W.N.: Some identities in combinatory analysis. Proc. London Math. Soc. 49(2), 421–425 (1947)

  4. Bressoud, D.M.: The Borwein conjecture and partitions with prescribed hook differences. (English. English summary) The Foata Festschrift. Electron. J. Combin. 3(2) (1996), Research Paper 4, approx. 14 pp. (electronic).

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois, 61801

    Alexandru Zaharescu

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  1. Alexandru Zaharescu
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Correspondence to Alexandru Zaharescu.

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2000 Mathematics Subject Classification Primary—11P99; Secondary—11B75

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Zaharescu, A. Borwein's conjecture on average over arithmetic progressions. Ramanujan J 11, 95–102 (2006). https://doi.org/10.1007/s11139-006-5309-8

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  • DOI: https://doi.org/10.1007/s11139-006-5309-8

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