Geoffrey B. Campbell
Dr Geoffrey B Campbell
Long Term Campus Visitor
PhD (ANU), GDip Internet and Web Comp (RMIT University)
email geoffrey.campbell@anu.edu.au
email geoffreycampbell@yahoo.com
call +61408316592

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  Groups

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). Includes brief bios on Srinivasa Ramanujan, George E Andrews, Rodney J Baxter and Jonathan 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 https://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:

47            CAMPBELL, G. B. Fun with numbers 13: 6th and 8th Power Taxicab Number variants, Aust. Math. Soc. Gazette, Volume 51, No5, November 2024. (to appear) (https://austms.org.au/publications/gazette/gazette515/)

46            CAMPBELL, G. B. Fun with numbers: Multigrade Semi-Magic Squares, Aust. Math. Soc. Gazette, Volume 51, No4, September 2024. (https://austms.org.au/publications/gazette/gazette514/)

45            CAMPBELL, G. B. Fun with numbers: Identities for number bases 6, 14, and 15, Aust. Math. Soc. Gazette, Volume 51, No3, 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 https://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 Euler’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 xy=yx and xy yx = vw wv,  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 xyyx = vwwv,  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 x5 - (x+1)5 - (x+2)5 + (x+3)5 = 5m + 5n, 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.)