Publications

1. 2026
   Explicit Brauer–Manin obstructions on plane quarticswith Brendan Creutz · PreprintarXiv
2. 2026
   Arithmetic, geometry, cryptography and coding theorywith David Kohel and Chloe Martindale (eds.) · Proceedings of the 19th International Conference AGC²T, CIRM, Marseille, June 5–9, 2023. Contemp. Math. 832, vii+209 pp.doi
3. 2025
   On (2,2)-decomposable genus 4 Jacobianswith Avinash Kulkarni · Canad. J. Math. (2025), 1–26arXivdoidata
4. 2025
   Local Euler characteristics of $A_n$-singularities and their application to hyperbolicitywith Nathan Ilten and Zhe Xu · Épijournal Géom. Algébrique 9 (2025), Art. 2arXivdoidata
5. 2024
   Rigorous numerical integration of algebraic functionswith Linden Disney-Hogg and Wuqian Effie Gao · J. Softw. Algebra Geom. 14 (2024), 117–132arXivdoi
6. 2023
   Genus two curves with full $\sqrt{3}$-level structure and Tate–Shafarevich groupswith E. Victor Flynn and Ari Shnidman · Selecta Math. 29 (2023), 42arXivdoi
7. 2022
   Explicit computation of symmetric differentials and its application to quasihyperbolicitywith Jordan Thomas and Anthony Várilly-Alvarado · Algebra Number Theory 16 (2022), no. 6, 1377–1405arXivdoi
8. 2022
   Twists of the Burkhardt quartic threefoldwith Eugene Filatov · Res. Number Theory 8 (2022), no. 4, 73arXivdoi
9. 2020
   Two-cover descent on plane quartics with rational bitangentswith Daniel Lewis · ANTS XIV, Open Book Series 4 (2020), 73–89arXivdoicodeslidesvideoyoutube
10. 2020
    Prym varieties of genus four curveswith Emre Can Sertöz · Trans. Amer. Math. Soc. 373 (2020), 149–183arXivdoi
11. 2019
    Numerical computation of endomorphism rings of Jacobianswith Jeroen Sijsling and Alexandre Zotine · ANTS XIII, Open Book Series 2 (2019), 155–171arXivdoicode
12. 2018
    Arithmetic aspects of the Burkhardt quartic threefoldwith Brett Nasserden · J. London Math. Soc. 98 (2018), 536–556arXivdoidata
13. 2018
    Visibility of 4-covers of elliptic curveswith Tom Fisher · Res. Number Theory 4 (2018), 11arXivdoi
14. 2016
    Generalized explicit descent and its application to curves of genus 3with Bjorn Poonen and Michael Stoll · Forum Math. Sigma 4 (2016), e6, 80 pp.arXivdoi
15. 2014
    Descent via (3,3)-isogeny on Jacobians of genus 2 curveswith E. Victor Flynn and Damiano Testa · Acta Arith. 165 (2014), 201–223arXivdoi
16. 2013
    Success and challenges in determining the rational points on curvesANTS X, Open Book Series 1 (2013), 187–212doi
17. 2013
    On congruent primes and class numbers of imaginary quadratic fieldswith Brett Hemenway · Acta Arith. 159 (2013), 63–87arXivdoi
18. 2012
    Minimal models for rational functions in a dynamical settingwith Alexander Molnar · LMS J. Comput. Math. 15 (2012), 400–417arXivdoidata
19. 2012
    Transcendence of generating functions whose coefficients are multiplicativewith Jason P. Bell and Michael Coons · Trans. Amer. Math. Soc. 364 (2012), 933–959arXivdoi
20. 2011
    The arithmetic of genus two curves with (4,4)-split Jacobianswith Kevin Doerksen · Canad. J. Math. 63 (2011), 992–1021arXivdoidata
21. 2010
    The Mordell–Weil sieve: proving non-existence of rational points on curveswith Michael Stoll · LMS J. Comput. Math. 13 (2010), 272–306arXivdoi
22. 2010
    Visualizing elements of Sha[3] in genus 2 Jacobianswith Sander R. Dahmen · ANTS IX, Lecture Notes in Comput. Sci. 6197, Springer (2010), 110–125arXivdoi
23. 2009
    Two-cover descent on hyperelliptic curveswith Michael Stoll · Math. Comp. 78 (2009), 2347–2370arXivdoidata
24. 2008
    Deciding existence of rational points on curves: an experimentwith Michael Stoll · Experiment. Math. 17 (2008), no. 2, 181–189open accessarXivdoidata
25. 2008
    The arithmetic of Prym varieties in genus 3Compositio Math. 144 (2008), 317–338arXivdoidata
26. 2007
    The Brauer–Manin obstruction and Sha[2]with Martin J. Bright, E. Victor Flynn and Adam Logan · LMS J. Comput. Math. 10 (2007), 354–377 Electronic resources are in Appendix A of the paper.doidata
27. 2007
    Rational points on twists of $X_0(63)$with Julio Fernández, Josep González and Joan-Carles Lario · Acta Arith. 126 (2007), no. 4, 361–385preprintdoi
28. 2006
    Arithmetic progressions consisting of unlike powerswith Kálmán Győry, Lajos Hajdu and Szabolcs Tengely · Indag. Math. 17 (2006), no. 4, 539–555arXivdoi
29. 2006
    On finiteness conjectures for endomorphism algebras of abelian surfaceswith E. Victor Flynn, Josep González and Victor Rotger · Math. Proc. Cambridge Philos. Soc. 141 (2006), 383–408arXivdoidata
30. 2006
    Powers from products of consecutive terms in arithmetic progressionwith Michael A. Bennett, Kálmán Győry and Lajos Hajdu · Proc. London Math. Soc. (3) 92 (2006), no. 2, 273–306pdfdoi
31. 2006
    Exhibiting Sha[2] on hyperelliptic Jacobianswith E. Victor Flynn · J. Number Theory 118 (2006), 266–291open accessdoi
32. 2006
    Some ternary Diophantine equations of signature $(n,n,2)$In Discovering Mathematics with Magma, W. Bosma, J. Cannon (eds.), Algorithms Comput. Math. 19, Springer (2006), 63–91pdfdoidata
33. 2005
    The primitive solutions to $x^3+y^9=z^2$J. Number Theory 111 (2005), 179–189arXivdoitranscript
34. 2005
    Towers of 2-covers of hyperelliptic curveswith E. Victor Flynn · Trans. Amer. Math. Soc. 357 (2005), 4329–4347preprintdoi
35. 2004
    Rational divisors in rational divisor classeswith E. Victor Flynn · ANTS VI, D. Buell (ed.), Lecture Notes in Comput. Sci. 3076, Springer (2004), 132–139open accessdoi
36. 2004
    Visualising Sha[2] in abelian surfacesMath. Comp. 73 (2004), no. 247, 1459–1476arXivdoidata
37. 2003
    Chabauty methods using elliptic curvesJ. Reine Angew. Math. 562 (2003), 27–49 The 2003 volumes of Crelle seem to have fallen off the map, so as a stop-gap measure there is a cached copy (no copyright infringement intended).cacheddoi
38. 2003
    $N$-covers of hyperelliptic curveswith E. Victor Flynn · Math. Proc. Cambridge Philos. Soc. 134 (2003), no. 3, 397–405open accessdoi
39. 2002
    Chabauty methods and covering techniques applied to generalized Fermat equationsCWI Tract 133, 77 pp.link
40. 2002
    Trinomials $ax^7+bx+c$ and $ax^8+bx+c$ with Galois groups of order 168 and $8\cdot 168$with Noam D. Elkies · ANTS V, C. Fieker, D. R. Kohel (eds.), Lecture Notes in Comput. Sci. 2369, Springer (2002), 172–188doi
41. 2000
    On powers as sums of two cubesANTS IV, W. Bosma (ed.), Lecture Notes in Comput. Sci. 1838, Springer (2000), 169–184 Associated files: prf335.g, tor334.mpl, prf335.mpl.psdoi
42. 1999a
    Chabauty methods and covering techniques applied to generalised Fermat equationsPhD thesis, Leiden University Also the accompanying stellingen (in Dutch).pdfpserrata
43. 1999b
    The Diophantine equations $x^2\pm y^4=\pm z^6$ and $x^2+y^8=z^3$Compositio Math. 118 (1999), 305–321doifiles
44. 1999
    Throughput of ADSL modemswith H. J. Broersma, J. L. Hurink, L. E. Meester, S. S. op de Beek and J. H. Westhuis · Proceedings of the 33rd European Study Group with Industry, Syllabus 46, CWI, Amsterdam (1999), 11–26open access
45. 1995
    Generalization of the ABC-conjectureMaster’s thesis, Leiden Universitypdfps

See also the theses of my students.