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.


I have given links to “unofficial electronic versions” of several 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 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. Principally polarized squares of elliptic curves with field of moduli equal to Q (with Alexandre Gélin and Christophe Ritzenthaler). To appear in the Proceedings of the 13th Algorithmic Number Theory Symposium (Madison, WI 2018).
  2. Hasse–Witt and Cartier–Manin matrices: A warning and a request (with Jeffrey D. Achter), arXiv:1710.10726 [math.NT]. GTo appear in the Proceedings of the Arithmetic, Geometry, Crytography, and Coding Theory (Luminy, 2017).

Papers in preparation:

  1. (with Victor Rotger): What can be recovered on a curve from its unpolarized Jacobian?, in preparation.
  2. On the distribution of Frobenius eigenvalues of principally-polarized abelian varieties, in preparation.
  3. The intersection of all Humbert surfaces with square invariant, in preparation.
  4. Genus-two curves with maps of every degree to a fixed elliptic curve, in preparation.
Books edited:
  1. Yves Aubry, Everett W. Howe, and Christophe Ritzenthaler, eds.: Arithmetic, Geometry, Cryptography, and Coding Theory: AGC2T-16, Contemporary Mathematics Series, American Mathematical Society, Providence, RI, 2018 (to appear).
  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 in print:
  1. 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.
  2. Curves of medium genus with many points, Finite Fields Appl. 47 (2017) 145–160.
  3. 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.
  4. 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.
  5. Optimal quotients and surjections of Mordell–Weil groups, J. Number Theory 166 (2016) 85–92. MR 3486265, Zbl 06572129.
  6. 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.
  7. Genus-2 Jacobians with torsion points of large order, Bull. London Math. Soc. 47 (2015) 127–135. MR 3312971, Zbl 1319.14030.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. On the nonexistence of certain curves of genus two, Compositio Math. 140 (2004) 581–592. MR 2005a:11088, Zbl 1067.11035.
  23. 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.
  24. 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.
  25. 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.
  26. 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.
  27. Plane quartics with Jacobians isomorphic to a hyperelliptic Jacobian, Proc. Amer. Math. Soc. 129 (2001) 1647–1657. MR 2002a:14028, Zbl 0974.14021.
  28. Higher-order Carmichael numbers, Math. Comp. 69 (2000) 1711–1719. MR 2001a:11012, Zbl 0966.11006.
  29. 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.
  30. 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.
  31. Constructing distinct curves with isomorphic Jacobians, J. Number Theory 56 (1996) 381–390. MR 97d:11101, Zbl 0842.14019.
  32. Kernels of polarizations of abelian varieties over finite fields, J. Algebraic Geom. 5 (1996) 583–608. MR 96m:14063, Zbl 0911.11031.
  33. 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.
  34. 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.
  35. The Weil pairing and the Hilbert symbol, Math. Ann. 305 (1996) 387–392. MR 97b:11084, Zbl 0854.11031.
  36. Bounds on polarizations of abelian varieties over finite fields, J. Reine Angew. Math. 467 (1995) 149–155. MR 96i:11064, Zbl 0832.14033.
  37. Constructing distinct curves with isomorphic Jacobians in characteristic zero, Internat. Math. Res. Notices 1995 173–180. MR 96f:14030, Zbl 0832.14019.
  38. Principally polarized ordinary abelian varieties over finite fields, Trans. Amer. Math. Soc. 347 (1995) 2361–2401. MR 96i:11065, Zbl 0859.14016.
  39. On the group orders of elliptic curves over finite fields, Compositio Math. 85 (1993) 229–247. MR 94a:11089, Zbl 0793.14023.
  40. 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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