The Ramanujan Journal

, Volume 47, Issue 3, pp 565–588 | Cite as

On the restricted partition function

  • Mircea CimpoeaşEmail author
  • Florin Nicolae


For a vector \(\mathbf a = (a_1,\ldots ,a_r)\) of positive integers, we prove formulas for the restricted partition function \(p_{\mathbf a}(n): = \) the number of integer solutions \((x_1,\dots ,x_r)\) to \(\sum _{j=1}^r a_jx_j=n\) with \(x_1\ge 0, \ldots , x_r\ge 0\) and its polynomial part.


Restricted partition function Barnes zeta function Quasi-polynomial 

Mathematics Subject Classification

Primary 11P81 Secondary 11P82 11P83 



We thank the referee for the valuable suggestions which helped to improve our paper.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Simion Stoilow Institute of MathematicsBucharestRomania

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