## Rocky Mountain Journal of Mathematics

### Note on the truncated generalizations of Gauss's square exponent theorem

Shane Chern

#### Abstract

In this note, we investigate Liu's work on the truncated Gaussian square exponent theorem and obtain more truncations. We also discuss some possible multiple summation extensions of Liu's results.

#### Article information

Source
Rocky Mountain J. Math., Volume 48, Number 7 (2018), 2211-2222.

Dates
First available in Project Euclid: 14 December 2018

https://projecteuclid.org/euclid.rmjm/1544756808

Digital Object Identifier
doi:10.1216/RMJ-2018-48-7-2211

Mathematical Reviews number (MathSciNet)
MR3892131

Zentralblatt MATH identifier
06999261

#### Citation

Chern, Shane. Note on the truncated generalizations of Gauss's square exponent theorem. Rocky Mountain J. Math. 48 (2018), no. 7, 2211--2222. doi:10.1216/RMJ-2018-48-7-2211. https://projecteuclid.org/euclid.rmjm/1544756808

#### References

• G.E. Andrews, The theory of partitions, Cambridge University Press, Cambridge, 1998.
• G.E. Andrews and M. Merca, The truncated pentagonal number theorem, J. Combin. Th. 119 (2012), 1639–1643.
• ––––, Truncated theta series and a problem of Guo and Zeng, J. Combin. Th. 154 (2018), 610–619.
• A. Berkovich and F.G. Garvan, Some observations on Dyson's new symmetries of partitions, J. Combin. Th. 100 (2002), 61–93.
• S.H. Chan, T.P.N. Ho and R. Mao, Truncated series from the quintuple product identity, J. Num. Th. 169 (2016), 420–438.
• S.B. Ekhad and D. Zeilberger, The number of solutions of $X^2=0$ in triangular matrices over $GF(q)$, Electr. J. Combin. 3 (1996).
• V.J.W. Guo and J. Zeng, Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas, Discr. Math. 308 (2008), 4069–4078.
• ––––, Two truncated identities of Gauss, J. Combin. Th. 120 (2013), 700–707.
• T.Y. He, K.Q. Ji and W.J.T. Zang, Bilateral truncated Jacobi's identity, European J. Combin. 51 (2016), 255–267.
• F. Jouhet, Shifted versions of the Bailey and well-poised Bailey lemmas, Ramanujan J. 23 (2010), 315–333.
• L.W. Kolitsch, Another approach to the truncated pentagonal number theorem, Int. J. Num. Th. 11 (2015), 1563–1569.
• J.C. Liu, Some finite generalizations of Euler's pentagonal number theorem, Czechoslovak Math. J. 67 (2017), 525–531.
• ––––, Some finite generalizations of Gauss's square exponent identity, Rocky Mountain J. Math. 47 (2017), 2723–2730.
• R. Mao, Proofs of two conjectures on truncated series, J. Combin. Th. 130 (2015), 15–25.
• A. Riese, qMultiSum–A package for proving $q$-hypergeometric multiple summation identities, J. Symbol. Comp. 35 (2003), 349–376.
• S.O. Warnaar, $q$-Hypergeometric proofs of polynomial analogues of the triple product identity, Lebesgue's identity and Euler's pentagonal number theorem, Ramanujan J. 8 (2004), 467–474.
• A.J. Yee, A truncated Jacobi triple product theorem, J. Combin. Th. 130 (2015), 1–14.