- CAMPBELL, G. B. Generalization of a formula of Hardy, La Trobe University
preprints no 79-5, 1979 (written whilst a young student.) This paper was
accepted for publication at Aequationes Mathematicae, but by then the author had left
university, and was unable to carry out the required minor changes. Papers
numbered 4 and 5 below revisit this topic. Whilst 4 appeared in print, the
results in 5 were considered too compressed and in need of further
elucidation.
- CAMPBELL, G. B. Multiplicative functions over Riemann zeta function products,
J. Ramanujan Soc. 7 No. 1, 1992, 52-63.
- CAMPBELL, G. B. Dirichlet summations and products over primes,
Internat. J. Math. & Math. Sci., Vol 16, No
2, 1993, 359-372.
- CAMPBELL, G. B. A generalised formula of Hardy, Int. J. Math. Math. Sci., Vol 17, No 2, 1994, 369-378.
- CAMPBELL, G. B. Formulae with functions exhibiting self-similarity, Research
Paper preprint series, Centre for Mathematics and its Applications, The
Australian National University, 1993.
- 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.
- CAMPBELL, G. B. Infinite products over visible lattice points, Internat. J.
Math. & Math. Sci., Vol 17, No 4, 1994,
637-654.
- CAMPBELL, G. B. A closer look at some new identities, Internat. J. Math. &
Math. Sci., Vol 21, No 3, 1998, pp581-586.
- CAMPBELL, G. B. A generalized Ramanujan arithmetical
function, and Jordan’s totient, Internat. J.
Math. & Math. Sci., (was to appear 2000 but
was withdrawn by the journal due to page charges)
- CAMPBELL, G. B. Dirichlet series analogues of q-series,
Internat. J. of Math, & Math. Sci., (was to
appear 2000 but was withdrawn by the journal due to page charges)
- CAMPBELL, G. B. Infinite products over hyperpyramid
lattices, Internat. J. Math. & Math. Sci.,
Vol 23, No 4, 2000, 271-277.
- CAMPBELL, G. B. Further Dirichlet series analogues of
q-series, Internat. J. of Math, & Math. Sci.,
(was to appear 2000 but was withdrawn by the journal due to page charges)
- CAMPBELL, G. B. Dirichlet series analogues of bilateral q-series,
Internat. J. of Math, & Math. Sci., (was to
appear 2000 but was withdrawn by the journal due to page charges)
- CAMPBELL, G. B. Dirichlet series related D-analogues of the
q-gamma and q-beta functions, Internat. J. Math. & Math. Sci., (was to appear 2000 but was withdrawn by the
journal due to page charges)
- CAMPBELL, G. B. Partial Euler Product Dirichlet series
analogues of q-series, Internat. J. of Math, & Math. Sci., (was to appear 2000 but was withdrawn by the
journal due to page charges)
- CAMPBELL, G. B. Further cases of Dirichlet series
analogues of q-series, Internat. J. of Math, & Math. Sci., (was to appear 2000 but was withdrawn by the
journal due to page charges)
- CAMPBELL, G. B. Visible point vector summations from hypercube and hyperpyramid lattices, Internat. J. Math. &
Math. Sci., Vol 21, No 4, 741-748, 1998.
- CAMPBELL, G. B. Combinatorial identities related to vector partitions,
Internat. J. of Math, & Math. Sci., (was to
appear 2000 but was withdrawn by the journal due to page charges)
- 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.
- CAMPBELL, G. B. Combinatorial Infinite Products in Several Variables over Visible
Lattice Points, Lecture Notes in Mathematics, Springer Verlag, New York, (Submitted 1998 as a monograph, but
misplaced by the editors. An updated version of 160 pages in length has
been resubmitted.)
- CAMPBELL, G. B. Combinatorial Identities in Number Theory related to q-series and
Arithmetical functions, Bull. Austral. Math. Soc., Vol. 58, (1998)
pp345-347.
- CAMPBELL, G. B. A New Class of Identities akin to q-Series in Several Variables,
Research paper no (to be determined), Centre for Mathematics and its applications,
The Australian National University, 1998.
- CAMPBELL, G. B. Dirichlet series analogues of q-series,
Mathematics Research Report No 2000.014, (this was a 59 page portion of
the manuscript submitted in 1999 as a monograph to Lecture Notes in
Mathematics, Springer Verlag, New York The
manuscript went missing at Springer Verlag along
with the one cited above at 20, but is to be resubmitted)
- CAMPBELL, G. B. Characterization of three dimensional images by visible point
vector projections, unpublished paper, 2001. (The author liaised with
the Supercomputer Lab staff at ANU in 2000 in order to establish a
perspective on the value of the ideas underlying this work.)
- CAMPBELL, G. B. An Euler Product transform applied to q series, Ramanujan J (2006) 12:267-293.
- 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.
- CAMPBELL, G. B. Generating Functions for Vector Partitions, Submitted 2006 to Int J Number Theory.
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