Publications

Books and Lecture Notes

The Collected Papers of Hans Arnold Heilbronn (with R.A. Smith). J. Wiley & Sons, New York, 1988. XVI + 608 pp.
Math 211: Algebraic Methods 14th ed. (with N. Pullman, N. Rice). Campus Bookstore, Queen's University at Kingston, 2015). iii + 421 pp.
Lectures on Applications of Modular Forms to Number Theory. (PDF 570KB) Course Notes for Math 817: Modular Forms (Winter 2005), 94pp.
Lectures on Quadratic Forms and Elliptic Curves I. (PDF 618KB) Course notes {part I) for Math 812 (Fall 2008), 102pp.

Preprints

• The number of curves of genus 2 with a given refined Humbert invariant (with H. Kir).   March 2026, 25pp.
    Abstract: n/a.   Preprint: pdf file
• Principal polarizations on abelian product surfaces,   January 2023; revised October 2024, 19pp.
    Abstract: n/a.   Preprint: pdf file
• Curves of genus 2 on abelian surfaces.   November 2023; revised July 2026, 40pp.
    Abstract: n/a.   Preprint: pdf file
• The refined Humbert invariant for abelian product surfaces with CM.   Revised April 2026, 24pp.
    Abstract: pdf file.   Preprint: pdf file
• Generalized Humbert schemes and intersections of Humbert surfaces.   July 2019; revised March 2023, 38pp.
    Abstract: n/a.   Preprint: pdf file
• Abelian subvarieties and the Shimura construction. Revised August 2005, 25pp.
    Abstract: pdf file;   Preprint: pdf file
• Mazur's question on mod 11 representations of elliptic curves (with O. Rizzo). Dec. 2000, 22pp.
    Abstract: pdf file;   Preprint: pdf file

Publications (after 1995)

• Subcovers of curves and moduli spaces.   In: Geometry at the Frontier Contemporary Math. 766 (2021), 229-250.
    Abstract: n/a; Preprint: pdf file
• Elliptic subcovers of curves of genus 2. I. The isogeny defect   Ann. math. Quebec. 43 (2019), 281-303.
    Abstract: pdf file; Preprint: pdf file
• Elliptic subcovers of curves of genus 2. II. The refined Humbert invariant   J. Number Theory 193 (2018), 302-335
    Abstract: pdf file; Preprint: pdf file
• Elliptic subcovers of hyperelliptic curves.   Math. Nachr. 290 (2017), 2890-2900.
    Abstract: pdf file; Preprint: pdf file
• The moduli spaces of Jacobians isomorphic to a product of two elliptic curves. Collectanea Math. 67 (2016), 21-54.
    Abstract: pdf file; Preprint: pdf file
• Normal forms of hyperelliptic curves of genus 3 (with G. Frey). Des. Codes Cryptogr. 77 (2015), 677-712.
    Abstract: n/a; Preprint: pdf file
• Jacobians isomorphic to a product of two elliptic curves and ternary quadratic forms. J. Number Theory 139 (2014), 138--174.
    Abstract: pdf file; Preprint: pdf file
• Simple geometricially split abelian surfaces over a finite field (with K.J. Chou).   J. Ramanujan Math. Soc. 29 (2014), 31-62.
    Abstract: pdf file; Preprint: pdf file
• Binary theta series and modular forms with complex multiplication.   Int. J. Number Theory 10 (2014), 1025-1042.
    Abstract: pdf file; Preprint: pdf file
• The space of binary theta series.   Ann. Sci. Math. Quebec 36 (2012), 501-534 (published 2013).
    Abstract: pdf file; Preprint: pdf file
• Idoneal numbers and some generalizations. Ann. Sci. Math. Quebec 35 (2011), 197-227.
    Abstract: n/a; Preprint: pdf file
• Products of CM elliptic curves. Collectanea Math. 62 (2011), 297-339.
    Abstract: n/a; Preprint: pdf file
• Curves of genus 2 with elliptic differentials and associated Hurwitz spaces (with G. Frey). In: Arithmetic, Geometry, Cryptography and Coding Theory (G. Lachaud et al.) Contemporary Math. 487 (2009), 33-81.
    Abstract: n/a; Preprint: pdf file
• Endomorphisms of Jacobians of modular curves. Archiv Math. 92 (2008), 206-237.
    Abstract: pdf file; Preprint: pdf file
• The number of genus 2 covers of an elliptic curve. Manuscripta Math. 121 (2006), 51-80.
    Abstract: pdf file; Preprint: pdf file
• The surjectivity of mod m Galois representations. Appendix to: The surjectivity of the Galois representations associated to non-CM elliptic curves by A. C. Cojocaru. Bull. Can. Math. Soc. 48 (2005), 16-31.
    Abstract: n/a; Preprint: pdf file
• The modular degree and the congruence number of a weight 2 modular form (with A. C. Cojocaru). Acta Arithmetica 114 (2004), 159-167.
    Abstract: n/a; Preprint: pdf file
• Hurwitz spaces of genus 2 covers of an elliptic curve. Collectanea Math. 54 (2003), 1-51.  
    Abstract: pdf file; Preprint: pdf file
• Projective p-adic representations of the K-rational geometric fundamental group (with G. Frey). Archiv der Mathematik 77 (2001), 32-46.
    Abstract: n/a. Preprint: pdf file
• Curves with infinite K-rational geometric fundamental group (with G. Frey and H. Voelklein). In: Aspects of Galois Theory - Proceedings of the Conference on Galois Groups 1997, University of Florida, Gainesville, Florida (H.Voelklein, D. Harbater, P. Mueller, J. Thompson)  London Math. Soc. Lecture Notes 256 (1999), 85-118.
    Abstract: n/a. Preprint: pdf file
• Modular diagonal quotient surfaces (with W. Schanz). Mathematische Zeitschrift 227 (1998), 337-366.
    Abstract: n/a. Preprint: pdf file
• Diagonal quotient surfaces (with W. Schanz). Manuscripta Mathematica 93 (1997), 67-108.
    Abstract: n/a. Preprint: pdf file
• The existence of curves of genus 2 with elliptic differentials. J. Number Theory 64 (1997), 130-161.
    Abstract: n/a. Preprint: pdf file
• The number of curves of genus 2 with elliptic differentials. J. reine angew. Math. 485 (1997), 93-121.
    Abstract: n/a. Preprint: pdf file
• Fermat's Last Theorem (Coleman-Ellis Lecture, November 1996). Queen's Mathematical Communicator, Summer 1997, 1-8.
    Abstract: n/a. Preprint: pdf file

Publications (before 1995)

• Elliptic curves on abelian surfaces. Manuscripta Mathematica 84 (1994), 199-223.
    Abstract: n/a. Preprint: pdf file.
• Idempotent relations among arithmetic invariants attached to number fields and algebraic varieties (with M. Rosen). J. Number Theory 46 (1994), 230-254. 
• Discriminants of Hermitian R[G]-modules and Brauer's class number relation. In: Algebra and Number Theory - Proceedings of a Conference at the IEM Essen, 1992 (G. Frey, J. Ritter, eds) W. de Gruyter, Berlin, 1994, pp. 43-135.
    Abstract: n/a. Preprint: pdf file.
• Curves of genus 2 covering elliptic curves and an arithmetical application (with G. Frey). In: Arithmetic Algebraic Geometry (G. van der Geer, F. Oort, J. Steenbrink, eds.) Progress in Math. 89, Birkhauser, Boston, 1990, pp. 153-176.
• The Hilbert-Burch Theorem (with A. V. Geramita). In: The Curves Seminar at Queen's VI. Queen's Papers in Pure and Appl. Math 89 (1989), pp. A92-A96.
• Potential Theory on Curves. In: Theorie des Nombres/Number Theory. W. de Gruyter, Berlin, 1989, pp. 475-543.
• Idempotent relations and factors of Jacobians (with M. Rosen). Mathematische Annalen 284 (1989), 307-327.
• Unramified double covers of hyperelliptic Klein surfaces. C. R. Math. Rep. Acad. Sci. Canada 9 (1987), 133-138.
• The Galois module structure of the space of holomorphic differentials of a curve. J. reine angew. Math. 367 (1986), 187-206. 
• Bounds on the number of non-rational subfields of a function field. Inventiones mathematicae 85 (1986), 185-198.
• Relations between the genera and the Hasse-Witt invariants of Galois coverings of curves. Can. Math. Bull. 28 (1985), 321-327. 
• Weil heights, Neron pairings and v-metrics on curves. Rocky Mountain J. 15 (1985),  417-443.
• Robert Arnold Smith 23.1.1937- 30.3.1983 (Obituary). Rocky Mountain J. 15 (1985),  413-415.
• On Castelnuovo's equivalence defect. J. reine angew. Math. 352 (1984), 24-70.
• Nonstandard methods in Diophantine geometry. In: Journees Arithmetiques, 1980. London Math. Soc. Lecture Notes 56 (1982), 322-342. 
• Eine Verallgemeinerung des Satzes von Castelnuovo-Severi. J. reine angew. Math. 318 (1980), 178-220,  
• Nonstandard Diophantine Geometry. In: Proc. Queen's Number Theory Conference, 1979. Queen's Papers in Pure and Appl. Math 54 (1980), pp. 129-172.