Associate Professor Daniel Delbourgo

Associate Professor/Graduate Adviser (Mathematics)

Contact Details

Room: G.3.04
Phone: +64 7 838 4425
Extension: 4425
Fax: +64 7 838 4666

Research Interests

Number theory is as relevant today as it was two millennia ago, with the advent of high-powered computing and cryptography. Dr Delbourgo's research interests lie in the area of elliptic curves and modular forms. His work applies ideas from classical Iwasawa theory and Galois representations, to study the arithmetic behaviour of invariants arising from these objects. He is also interested in the special values of these L-functions, as there is a rich vein of conjectures connecting these L-values with elements in K-groups.


D. Delbourgo, On trivial p-adic zeroes for elliptic curves over Kummer extensions, New Zealand Journal of Mathematics 45 (2015), 33-38.

D. Delbourgo and A. Lei, Transition formulae for ranks of abelian varieties, to appear in the Rocky Mountain J. of Math. (in 2015), 27 pages; available at

D. Delbourgo, Exceptional zeros of p-adic L-functions over non-abelian extensions, to appear in the Glasgow Math. Journal (in 2015), 48 pages; available at

D. Delbourgo and L. Peters, Higher order congruences amongst Hasse-Weil L-values, Journal of the Australian Mathematical Society 98 (2015), 1-38.

K. Broughan, D. Delbourgo, and Q. Zhou, A conjecture of De Koninck regarding particular square values of the sum of divisors function, Journal of Number Theory 137 (2014), 50-66.

D. Delbourgo and K. Morgan, Algebraic invariants arising from the chromatic polynomial of theta graphs, Australasian Journal of Combinatorics 59 (2014), 293-310.

K. Broughan and D. Delbourgo, On the ratio of the sum of divisors and Euler's totient function I, Journal of Integer Sequences 16 #13.8.8 (2013), 16 pages.

K. Broughan, D. Delbourgo, and Q. Zhou, Improving the Chen and Chen result for odd perfect numbers, Integers 13 (2013), 8 pages.

D. Delbourgo, Millennium Prize: the Birch and Swinnerton-Dyer Conjecture, published in The Conversation (2011); available at

D. Delbourgo and T.Ward, The growth of CM periods over false Tate extensions, Experimental Mathematics 19 no. 2 (2010), 195-210.

D. Delbourgo, The convergence of Euler products over p-adic number fields, Proceedings of the Edinburgh Mathematical Society 52 no. 3 (2009), 583-606.

D. Delbourgo, Zeta-functions through the 2-adic looking glass, Gazette of the Australian Mathematical Society 36 no. 4 (2009), 266-272.

D. Delbourgo, Accouplements de poids p-adiques sur les pro-jacobiennes, C. R. Acad´emie des Sciences Paris, Ser I 346 (2008), 819-824.

D. Delbourgo, Elliptic curves and big Galois representations, LMS Lecture Notes in Mathematics Series, Book Number 356, Cambridge University Press (2008), 288 pages, ISBN 978-0-521-72866-9 paperback.

D. Delbourgo and T. Ward, Non-abelian congruences between L-values of elliptic curves, Annales de l'Institut Fourier 58 no. 3 (2008), 1023-1055.

D. Delbourgo and P. Smith, Kummer theory for big Galois representations, Mathematical Proceedings of the Cambridge Philosophical Society 142 (2007), 205-217.

D. Delbourgo, Λ-adic Euler characteristics of elliptic curves, Documenta Mathematica, extra volume in honour of J.H. Coates birthday (2006), 301-323.

D. Delbourgo, A Dirichlet series expansion for the p-adic zeta-function, Journal of the Australian Mathematical Society 81 (2006), 215-224.

D. Delbourgo, On the p-adic Birch and Swinnerton-Dyer conjecture for non-semistable reduction, Journal of Number Theory 95 no. 1 (2002), 38-71.

D. Delbourgo, L-invariants arising from p-adic measures of Sym2E, Glasgow Mathematical Journal 44 no. 1 (2001), 45-64.

D. Delbourgo, Iwasawa theory for elliptic curves at unstable primes, Compositio Mathematica 113 no. 2 (1998), 123-153.

D. Delbourgo, Non-archimedean L-functions at non-ordinary primes, Cambridge University PhD Thesis, United Kingdom (1997), 107 pages.

A. Dabrowski and D. Delbourgo, S-adic L-functions attached to the symmetric square of a newform, Proceedings of the London Mathematical Society 74 no. 3 (1997), 559-611.

D. Delbourgo and D. Elliott, On the approximate evaluation of Hadamard finite- part integrals, IMA Journal of Numerical Analysis 14 no. 4 (1994), 485-500.