Annotated bibliography.

I’ve listed all of my papers below; if you would like physical copies of any of them, just send me email (username=however, domain-name=alumni.caltech.edu) and ask. You can also get the Math Review links and Zentralblatt MATH links to all of my papers that have been reviewed. The links to the Mathematical Reviews here and below will only work if you are a subscriber. The links to the Zentralblatt MATH will work even if you are not a subscriber.

To find papers that cite mine, you can check my Google Scholar page.

I have given links to “unofficial electronic versions” of most of the papers below. These are preprint versions of the papers that are stored in the mathematics arXiv. Remember that the print versions of the papers are the versions of record, and please be aware that copyright in the papers remains held either by me, by my former employer, or by the publisher of the journal in which the paper appeared, depending.

You can also go directly to the arXiv’s list of all of the papers I submitted there.

Preprints:
  1. Doubly isogenous curves of genus two with a rational action of D6 (with Jeremy Booher, Andrew V. Sutherland, and José Felipe Voloch).
  2. Enumerating hyperelliptic curves over finite fields in quasilinear time.
  3. On the maximum gonality of a curve over a finite field (with Xander Faber and Jon Grantham).
  4. Purely inseparable Richelot isogenies (with Bradley W. Brock).

Books edited:

  1. Yves Aubry, Everett W. Howe, and Christophe Ritzenthaler, eds.: Arithmetic Geometry: Computation and Applications, Contemporary Mathematics 722, American Mathematical Society, Providence, RI, 2019.
  2. Everett W. Howe, Kristin E. Lauter, and Judy L. Walker, eds.: Algebraic Geometry for Coding Theory and Cryptography, Association for Women in Mathematics Series 9, Springer, Cham, 2017.
  3. Everett W. Howe and Kiran Kedlaya, eds.: ANTS X: Proceedings of the Tenth Algorithmic Number Theory Symposium, the Open Book Series 1, Mathematical Sciences Publishers, Berkeley, 2013. MR 3207404, Zbl 1295.11003.
Papers to appear:
  1. Refinements of Katz–Sarnak theory for the number of points on curves over finite fields (with Jonas Bergström, Elisa Lorenzo García, and Christophe Ritzenthaler), to appear in Canad. J. Math.
  2. Powers of 3 with few nonzero bits and a conjecture of Erdős (with Vassil S. Dimitrov), to appear in Rocky Mountain J. Math.
Papers in print:
  1. Lower bounds on the maximal number of rational points on curves over finite fields (with Jonas Bergström, Elisa Lorenzo García, and Christophe Ritzenthaler), Math. Proc. Cambridge Philos. Soc. 126 (2024) 213–238.
  2. Doubly isogenous genus-2 curves with D4-action (with Vishal Arul, Jeremy Booher, Steven R. Groen, Wanlin Li, Vlad Matei, Rachel Pries, and Caleb Springer), Math. Comp. 93 (2024) 347–381.
  3. Deducing information about curves over finite fields from their Weil polynomials, pp. 1–36 in: Curves over Finite Fields: Past, Present and Future (A. Bassa, E. Lorenzo García, and C. Ritzenthaler, eds.), Panoramas et synthèses 60, Société mathématique de France, Paris, 2023.
  4. Variations in the distribution of principally polarized abelian varieties among isogeny classes, Ann. H. Lebesgue 5 (2022) 677–702.
  5. Every positive integer is the order of an ordinary abelian variety over F2 (with Kiran S. Kedlaya), Res. Number Theory 7, 59 (2021).
  6. The maximum number of points on a curve of genus eight over the field of four elements, J. Number Theory 220 (2021) 320–329.
  7. Contributions to: Rational points on curves over finite fields (J.-P. Serre, edited by A. Bassa, E. Lorenzo García, C. Ritzenthaler, and R. Schoof, with contributions by Everett Howe, Joseph Oesterlé and Christophe Ritzenthaler, adapted and expanded from notes by Fernando Gouvêa of Serre’s 1985 lectures at Harvard University), Documents mathématiques 18, Société mathématique de France, Paris, 2020.
  8. Algorithms to enumerate superspecial Howe curves of genus 4 (with Momonari Kudo and Shushi Harashita), pp. 301–316 in: ANTS XIV: Proceedings of the Fourteenth Algorithmic Number Theory Symposium (S. Galbraith, ed.), the Open Book Series 4, Mathematical Sciences Publishers, Berkeley, 2020.
  9. Principally polarized squares of elliptic curves with field of moduli equal to Q (with Alexandre Gélin and Christophe Ritzenthaler), pp. 257–274 in: ANTS XIII: Proceedings of the Thirteenth Algorithmic Number Theory Symposium (R. Scheidler and J. Sorenson, eds.), the Open Book Series 2, Mathematical Sciences Publishers, Berkeley, 2019.
  10. Hasse–Witt and Cartier–Manin matrices: A warning and a request (with Jeffrey D. Achter), pp. 1–18 in: Arithmetic Geometry: Computation and Applications (Y. Aubry, E. W. Howe, and C. Ritzenthaler, eds.), Contemporary Mathematics 722, American Mathematical Society, Providence, RI, 2019.
  11. Locally recoverable codes from algebraic curves and surfaces (with Alexander Barg, Kathryn Haymaker, Gretchen L. Matthews, and Anthony Várilly-Alvarado), pp. 95–127 in: Algebraic Geometry for Coding Theory and Cryptography (E. W. Howe, K. E. Lauter, and J. L. Walker, eds.), Association for Women in Mathematics Series 9, Springer, Cham, 2017.
  12. Curves of medium genus with many points, Finite Fields Appl. 47 (2017) 145–160.
  13. Split abelian surfaces over finite fields and reductions of genus-2 curves (with Jeffrey D. Achter), Algebra Number Theory 11 (2017) 39–76. MR 3349314, Zbl 06679112.
  14. Quickly constructing curves of genus 4 with many points, pp. 149–173 in: Frobenius Distributions: Sato–Tate and Lang–Trotter conjectures (D. Kohel and I. Shparlinski, eds.), Contemporary Mathematics 663, American Mathematical Society, Providence, RI, 2016. MR 3502942, Zbl 06622651.
  15. Optimal quotients and surjections of Mordell–Weil groups, J. Number Theory 166 (2016) 85–92. MR 3486265, Zbl 06572129.
  16. Genus-2 curves and Jacobians with a given number of points (with Reinier Bröker, Kristin E. Lauter and Peter Stevenhagen), LMS J. Comput. Math. 18 (2015) 170–197. MR 3349314, Zbl 06399397.
  17. Genus-2 Jacobians with torsion points of large order, Bull. London Math. Soc. 47 (2015) 127–135. MR 3312971, Zbl 1319.14030.
  18. Genus bounds for curves with fixed Frobenius eigenvalues (with Noam D. Elkies and Christophe Ritzenthaler), Proc. Amer. Math. Soc. 142 (2014) 71–84. MR 3119182, Zbl 1286.14035.
  19. Constructing and tabulating dihedral function fields (with Colin Weir and Renate Scheidler), pp. 557–585 in: ANTS X: Proceedings of the Tenth Algorithmic Number Theory Symposium (E. W. Howe and K. Kedlaya, eds.), the Open Book Series 1, Mathematical Sciences Publishers, 2013. MR 3207431. Zbl 1345.11079.
  20. New methods for bounding the number of points on curves over finite fields (with Kristin E. Lauter), pp. 173–212 in: Geometry and Arithmetic (C. Faber, G. Farkas, and R. de Jong, eds.), European Mathematical Society, 2012. MR 2987661. Zbl 1317.11065.
  21. New bounds on the maximum number of points on genus-4 curves over small finite fields, pp. 69–86 in: Arithmetic, Geometry, Cryptography and Coding Theory (Y. Aubry, C. Ritzenthaler, and A. Zykin, eds.), Contemporary Mathematics 574, American Mathematical Society, Providence, RI, 2012. MR 2961401. Zbl 1317.11064.
  22. Lower bounds on the lengths of double-base representations (with Vassil S. Dimitrov), Proc. Amer. Math. Soc. 139 (2011) 3423–3430. MR 2012d:11194, Zbl 1263.11086.
  23. Appendix to: Robert Coleman and Ken McMurdy: Stable reduction of X0(p3), Algebra Number Theory 4 (2010) 357–431. MR 2011k:14022. Zbl 1215.11060.
  24. Characteristic polynomials of automorphisms of hyperelliptic curves (with Robert M. Guralnick), pp. 101–112 in: Arithmetic, Geometry, Cryptography and Coding Theory (G. Lachaud, C. Ritzenthaler, and M. A. Tsfasman, eds.), Contemporary Mathematics 487, American Mathematical Society, Providence, RI, 2009. MR 2010j:14060, Zbl 1184.14047.
  25. Jacobians in isogeny classes of abelian surfaces over finite fields (with Enric Nart and Christophe Ritzenthaler), Ann. Inst. Fourier (Grenoble) 59 (2009) 239–289. MR 2010b:11064, Zbl 1236.11058.
  26. Nonisomorphic curves that become isomorphic over extensions of coprime degrees (with Daniel Goldstein, Robert M. Guralnick, and Michael E. Zieve), J. Algebra 320 (2008) 2526–2558. MR 2009h:14051, Zbl 1160.14020.
  27. Supersingular genus-two curves over fields of characteristic three, pp. 49–69 in: Computational Arithmetic Geometry (K. E. Lauter and K. A. Ribet, eds.), Contemporary Mathematics 463, American Mathematical Society, Providence, RI, 2008. MR 2009j:11103, Zbl 1166.11020.
  28. Principally polarizable isogeny classes of abelian surfaces over finite fields (with Daniel Maisner, Enric Nart, and Christophe Ritzenthaler), Math. Res. Lett. 15 (2008) 121–127. MR 2006g:11125, Zbl 1145.11045.
  29. Pointless curves of genus three and four (with Kristin Lauter and Jaap Top), pp. 125–141 in: Algebra, Geometry, and Coding Theory (AGCT 2003) (Y. Aubry and G. Lachaud, eds.), Séminaires et Congrès 11, Société Mathématique de France, Paris, 2005. MR 2006g:11125, Zbl 1116.14010.
  30. Infinite families of pairs of curves over Q with isomorphic Jacobians, J. London Math. Soc. 72 (2005) 327–350. MR 2006b:11064, Zbl 1093.14041.
  31. Curves of every genus with many points, II: Asymptotically good families (with Noam D. Elkies, Andrew Kresch, Bjorn Poonen, Joseph L. Wetherell, and Michael E. Zieve), Duke Math. J. 122 (2004) 399–422. MR 2005h:11123, Zbl 1072.11041.
  32. On the nonexistence of certain curves of genus two, Compositio Math. 140 (2004) 581–592. MR 2005a:11088, Zbl 1067.11035.
  33. Improved upper bounds for the number of points on curves over finite fields (with Kristin E. Lauter), Ann. Inst. Fourier (Grenoble) 53 (2003) 1677–1737. MR 2005c:11079, Zbl 1065.11043. Corrigendum, Ann. Inst. Fourier (Grenoble) 57 (2007) 1019–1021.
  34. Appendix to: Daniel Maisner and Enric Nart: Abelian surfaces over finite fields as Jacobians, Experiment. Math. 11 (2002) 321–337. MR 2003k:14057. Zbl 1101.14056.
  35. On the existence of absolutely simple abelian varieties of a given dimension over an arbitrary field (with Hui June Zhu), J. Number Theory 92 (2002) 139–163. MR 2003g:11063, Zbl 0998.11031.
  36. Isogeny classes of abelian varieties with no principal polarizations, pp. 203–216 in: Moduli of Abelian Varieties (Carel Faber, Gerard van der Geer, and Frans Oort, eds.), Progr. Math 195, Birkhäuser, Basel, 2001. MR 2002g:11079, Zbl 1079.14531.
  37. Plane quartics with Jacobians isomorphic to a hyperelliptic Jacobian, Proc. Amer. Math. Soc. 129 (2001) 1647–1657. MR 2002a:14028, Zbl 0974.14021.
  38. Higher-order Carmichael numbers, Math. Comp. 69 (2000) 1711–1719. MR 2001a:11012, Zbl 0966.11006.
  39. Large torsion subgroups of split Jacobians of curves of genus two or three (with Franck Leprévost and Bjorn Poonen), Forum Math. 12 (2000) 315–364. MR 2001e:11071, Zbl 0983.11037.
  40. Real polynomials with all roots on the unit circle and abelian varieties over finite fields (with Stephen A. DiPippo), J. Number Theory 73 (1998) 426–450. MR 2000c:11101, Zbl 0931.11023. Corrigendum, J. Number Theory 83 (2000) 182.
  41. Constructing distinct curves with isomorphic Jacobians, J. Number Theory 56 (1996) 381–390. MR 97d:11101, Zbl 0842.14019.
  42. Kernels of polarizations of abelian varieties over finite fields, J. Algebraic Geom. 5 (1996) 583–608. MR 96m:14063, Zbl 0911.11031.
  43. My butter, garçon… (with Hendrik Lenstra and David Moulton), p. 28 in: A. van der Poorten, Notes on Fermat’s Last Theorem, John Wiley and Sons, New York 1996.
  44. Sous-groupes de torsion d’ordres élevés de Jacobiennes décomposables de courbes de genre 2 (with Franck Leprévost and Bjorn Poonen), C. R. Acad. Sci. Paris. Sér I Math. 323 (1996) 1031–1034. MR 97k:11097, Zbl 0895.11027.
  45. The Weil pairing and the Hilbert symbol, Math. Ann. 305 (1996) 387–392. MR 97b:11084, Zbl 0854.11031.
  46. Bounds on polarizations of abelian varieties over finite fields, J. Reine Angew. Math. 467 (1995) 149–155. MR 96i:11064, Zbl 0832.14033.
  47. Constructing distinct curves with isomorphic Jacobians in characteristic zero, Internat. Math. Res. Notices 1995 173–180. MR 96f:14030, Zbl 0832.14019.
  48. Principally polarized ordinary abelian varieties over finite fields, Trans. Amer. Math. Soc. 347 (1995) 2361–2401. MR 96i:11065, Zbl 0859.14016.
  49. On the group orders of elliptic curves over finite fields, Compositio Math. 85 (1993) 229–247. MR 94a:11089, Zbl 0793.14023.
  50. A new proof of Erdős’s theorem on monotone multiplicative functions, Amer. Math. Monthly 93 (1986) 593–595. MR 87k:11010, Zbl 0614.10001.

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