# Geoffrey B. Campbell

## Content navigation

## Affiliations

- Mathematical physics, Collaborator

## Research interests

Since 2022-24 written eleven "**Fun with Numbers**" articles for the **Gazette of the Australian Mathematical Society.**

Mathematics 2022-2024 to date a book monograph published 29 May 2024 entitled:* Partitions, Visible Point Vectors, and Ramanujan Functions (CRC Press, Taylor and Francis Group, Boca Raton, London, New York, A Chapman & Hall Book, ISBN: 978-1-032-00366-5 (hbk), ISBN: 978-1-032-00432-7 (pbk), ISBN: 978-1-003-17415-8 (ebk), DOI: 10.1201/9781003174158, published June 2024*.

*)*.

Foreword by

**Professor Dr Henk Koppelaar**(

**Delft University of Technology**). Bios on

**Srinivasa Ramanujan**,

**George E Andrews**,

**Rodney J Baxter**and

**Johnathan Borwein**. The book covers classical

*Integer Partitions*,

*Rogers-Ramanujan Partitions in Statistical Mechanics Solved Models*,

*Vector Partitions*and

*Visible Point Vector identities,*

*Plane Partitions*,

*Asymptotic Partition Formulas*, Chapters on

*Partition Congruences*,

*Ramanujan Continued Fractions*,

*Polylogarithms*,

*Parametric Euler sum identities*and

*Higher Dimensional Weighted Partition Identities*are included. Available for purchase at

**www.routledge.com/9781032003665**.

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I manage * LinkedIn Number Theory Group* located at https://www.linkedin.com/groups/4510047/.

I am an Administrator for the Facebook Group * Classical Mathematics* at https://www.facebook.com/groups/ClassicalMathematics.

## Teaching information

**External PhD Committee Member Washington State University.**

## Location

Room 2.73, Hanna Neumann Building 145

## Publications

**I am a published poet as well as a mathematics person. **__POEMS: __

Wrote and published *Words in Common *2010*. A *collection of *journal/magazine/anthology* published poems partly funded by **The Australia Council for the** **Arts**.The book was launched by **Professor Kevin Brophy, University of Melbourne**, Creative Writing Department. Edited by **Associate Professor Trevor Code**, **Deakin University**.

See a link with excerpts from the poems at http://bit.ly/3jAvlb8.

See a review of *Words In Common* by Canberra poet **Michael Byrne** at http://bit.ly/2MRlv8y.

__A SELECTION OF MY MATHEMATICAL PUBLICATIONS:__

45 CAMPBELL, G. B. *Fun with numbers: Identities for number bases 6, 14, and 15, *Aust. Math. Soc. Gazette, Volume 51, No3, (to appear) July 2024. (https://austms.org.au/publications/gazette/gazette513/)

44 CAMPBELL, G. B. *Vector Partitions, Visible Points, and Ramanujan Functions, *CRC Press, Taylor and Francis Group*, *Boca Raton, London, New York,* *A Chapman & Hall Book, ISBN: 978-1-032-00366-5 (hbk), ISBN: 978-1-032-00432-7 (pbk), ISBN: 978-1-003-17415-8 (ebk), DOI: 10.1201/9781003174158, *published*, 1st June 2024 www.routledge.com/9781032003665.

43 CAMPBELL, G. B. *Rogers-Ramanujan identities in Statistical Mechanics, * Math-Physics arxiv:2405.08425 [math-ph.CC-BY-NC-SA]. (https://arxiv.org/abs/2405.08425) May 2024.

42 CAMPBELL, G. B. *Fun with numbers: Some higher power sums and Eulerâ€™s failed conjecture, *Aust. Math. Soc. Gazette, Volume 51, No2, May 2024. (https://austms.org.au/publications/gazette/gazette512/)

41 CAMPBELL, G. B. *VPV Identities related to* **x ^{y}=y^{x}**

*and*

**x**

^{y}y^{x}= v^{w}w^{v}*,*arxiv:2404.10783 [math.CO]. (https://arxiv.org/abs/2404.10783) April 2024.

40 CAMPBELL, G. B. *Fun with numbers: Ternary or Base Three Identities, *Aust. Math. Soc. Gazette, Volume 50, No5, November 2023. (https://austms.org.au/publications/gazette/gazette505/)

39 CAMPBELL, G. B. *Visible Point Vector Partition Identities for Hyperpyramid Lattices, * arXiv:2309.16094 [math.CO]. (https://arxiv.org/abs/2309.16094) September 2023.

38 CAMPBELL, G. B. *Fun with numbers: Multigrade Sums with Carl Sagan and Pell Equations, *Aust. Math. Soc. Gazette, Volume 50, No4, September 2023. (https://austms.org.au/publications/gazette/gazette504/)

37 CAMPBELL, G. B. *Fun with numbers: Any rational is a sum of four 4th and four 5th powers, * Aust. Math. Soc. Gazette, Volume 50, No3, pp.117-119, July 2023. (https://austms.org.au/publications/gazette/gazette503/)

36 CAMPBELL, G. B. *Visible Point Partition Identities for Polylogarithms, and Parametric Euler Sums, * arXiv:2306.02241 [math.CO]. (https://arxiv.org/abs/2306.02241) June 2023.

35 CAMPBELL, G. B. *Fun with numbers: Revisiting an Eulerian Problem, * Aust. Math. Soc. Gazette, Volume 50, No2, pp.10-12, May 2023. (https://austms.org.au/publications/gazette/gazette502/)

34 CAMPBELL, G. B. *Fun with numbers: A base 7 identity, * Aust. Math. Soc. Gazette, Volume 50, No1, pp.13-14, March 2023. (https://austms.org.au/publications/gazette/gazette501/)

33 CAMPBELL, G. B. *Vector Partition Identities for 2D, 3D and nD Lattices, *arXiv:2302.01091v1 [math.CO], Feb 2023. (https://arxiv.org/abs/2302.01091)

32 CAMPBELL, G. B. *Continued Fractions for partition generating functions, *arXiv:2301.12945v1 [math.CO], Jan 2023. (https://arxiv.org/abs/2301.12945)

31 CAMPBELL, G. B. *Fun with numbers: Rational solutions to x ^{y}y^{x} = v^{w}w^{v}, * Aust. Math. Soc. Gazette, Volume 49, No5, pp210-211, November 2022. (https://austms.org.au/publications/gazette/gazette495/)

30 CAMPBELL, G. B. *Fun with numbers: Identities containing a certain algebraic form, * Aust. Math. Soc. Gazette, Volume 49, No4, pp162-163, September 2022. (https://austms.org.au/publications/gazette/gazette494/)

29 CAMPBELL, G. B. *Fun with numbers: Consecutive 6th powers and base 6 numbers, * Aust. Math. Soc. Gazette, Volume 49, No3, pp108-109, July 2022. (https://austms.org.au/publications/gazette/gazette493/)

28 CAMPBELL, G. B. *Fun with numbers: Ramanujan 6-10-8 identity, * Aust. Math. Soc. Gazette, Volume 49, No2, pp71-72, May 2022. (https://austms.org.au/publications/gazette/gazette492/)

27 CAMPBELL, G. B. *An interview with Rodney James Baxter*, Aust. Math. Soc. Gazette, Volume 47, No1, pp24-32, March 2020. (https://austms.org.au/wp-content/uploads/2020/07/471Web.pdf)

26. CAMPBELL, G. B. *Some n-space q-binomial theorem extensions and similar identities*, arXiv:1906.07526v1 [math.NT], Jun 2019. (https://arxiv.org/abs/1906.07526)

25 CAMPBELL, G. B. and ZUJEV, A. *The series that Ramanujan misunderstood*, arXiv:1610.03693v1 [math.NT], Oct 2016. (https://arxiv.org/abs/1610.03693v1)

24 CAMPBELL, G. B. and ZUJEV, A. *On integer solutions to x ^{5} - (x+1)^{5} - (x+2)^{5} + (x+3)^{5} = 5^{m} + 5^{n}*, arXiv:1603.00080v1 [math.NT], Feb 2016. (https://arxiv.org/abs/1603.00080v1)

23 CAMPBELL, G. B. and ZUJEV, A. *Some equations with features of digit reversal and powers*, arXiv:1602.06320v1 [math.NT], Feb 2016. (https://arxiv.org/abs/1602.06320v1)

22 CAMPBELL, G. B. and ZUJEV, A. *Gaussian integer solutions for the fifth power taxicab number problem*, arXiv:1511.07424v1 [math.NT], Nov 2015. (https://arxiv.org/abs/1511.07424v1)

21 CAMPBELL, G. B. and ZUJEV, A. *Variations on Ramanujan's nested radicals*, arXiv:1511.06865v1 [math.NT], Nov 2015. (https://arxiv.org/abs/1511.06865v1)

20 CAMPBELL, G. B. and ZUJEV, A. *A diophantine sum with factorials*, arXiv:1510.03056v2 [math.NT], Oct 2015. (https://arxiv.org/abs/1510.03056v2)

19 CAMPBELL, G. B. *The q-Dixon sum Dirichlet series analogue*, arXiv:1302.2664v1, Feb 2013. (https://arxiv.org/abs/1302.2664v1)

18 CAMPBELL, G. B. *Ramanujan and Eckford Cohen totients from Visible Point Identities*, arXiv:1212.2818v1 [math.NT], Dec 2012. (https://arxiv.org/abs/1212.2818v1)

17 CAMPBELL, G. B. *D-analogues of q-shifted factorial and the q-Kummer sum*, arXiv:1212.2248v1 [math.NT], Dec 2012. (https://arxiv.org/abs/1212.2248v1)

16 CAMPBELL, G. B. *Polylogarithm approaches to Riemann Zeta function zeroes*, arXiv:1212.2246v1 [math.NT], Dec 2012. (https://arxiv.org/abs/1212.2246v1)

15 CAMPBELL, G. B. *Dirichlet series analogues of q-shifted factorial and the q-Kummer sum*, Research paper 2003-6, Department of Mathematics, LaTrobe University, 2003.

14 CAMPBELL, G. B. *An Euler Product transform applied to q series*, Ramanujan J (2006) 12:267-293. (https://doi.org/10.1007/s11139-006-0078-y)

13 CAMPBELL, G. B. *A New Class of Identities akin to q-Series in Several Variables*, Research paper, Centre for Mathematics and its applications, The Australian National University, 1998.

12 CAMPBELL, G. B. *Combinatorial Identities in Number Theory related to q-series and Arithmetical functions*, Bull. Austral. Math. Soc., Vol. 58, (1998) pp345-347.

11 CAMPBELL, G. B. *On generating functions for vector partitions*, Research paper no 55-97, Centre for Mathematics and its applications, The Australian National University, 1997.

10 CAMPBELL, G. B. *Visible point vector summations from hypercube and hyperpyramid lattices*, Internat. J. Math. & Math. Sci., Vol 21, No 4, 741-748, 1998. (https://www.researchgate.net/publication/26536267_Visible_point_vector_summations_from_hypercube_and_hyperpyramid_lattices)

9 CAMPBELL, G. B. *Infinite products over hyperpyramid lattices*, Internat. J. Math. & Math. Sci., Vol 23, No 4, 2000, 271-277. (https://eudml.org/doc/48634)

8 CAMPBELL, G. B. *A closer look at some new identities*, Internat. J. Math. & Math. Sci., Vol 21, No 3, 1998, pp581-586. (https://www.researchgate.net/publication/26536244_A_closer_look_at_some_new_identities)

7 CAMPBELL, G. B. *Infinite products over visible lattice points*, Internat. J. Math. & Math. Sci., Vol 17, No 4, 1994, 637-654. (https://econpapers.repec.org/article/hinjijmms/705467.htm)

6 CAMPBELL, G. B. *A new class of infinite product, and Euler's totient*, Internat. J. Math. & Math. Sci., Vol 17, No 4, 1994, 417-422 (https://eudml.org/doc/47103).

5 CAMPBELL, G. B. *Formulae with functions exhibiting self-similarity*, Research Paper preprint series, Centre for Mathematics and its Applications, The Australian National University, 1993.

4 CAMPBELL, G. B. *A generalised formula of Hardy*, Int. J. Math. Math. Sci., Vol 17, No 2, 1994, 369-378 (https://eudml.org/doc/46967).

3 CAMPBELL, G. B. *Dirichlet summations and products over primes*, Internat. J. Math. & Math. Sci., Vol 16, No 2, 1993, 359-372 (https://ideas.repec.org/a/hin/jijmms/728942.html).

2 CAMPBELL, G. B. *Multiplicative functions over Riemann zeta function products*, J. Ramanujan Soc. 7 No. 1, 1992, 52-63 (https://jrms.ramanujanmathsociety.org/archieves/v7-1.html).

1 CAMPBELL, G. B. *Generalization of a formula of Hardy*, La Trobe University preprints no 79-5, 1979 (written whilst a young student.)