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Selected Publications
“A robust implementation for solving the ,” with Alejandra Alvarado, Angelos Koutsianas, Beth Malmskog, Christelle Vincent, Mckenzie West. In: Balakrishnan, J.S., Elkies, N., Hassett, B., Poonen, B., Sutherland, A.V., Voight, J. (Des) Arithmetic Geometry, Number Theory, and Computation. Simons Symposia. Springer, Cham, 2021, pp. 1-41. arXiv:1903.00977. [arXiv ] [doi.org ]
“Cyclic covers and Ihara’s Question ,” with Akio Tamagawa, Research in Number Theory 5 , 33 (2019). arXiv:1803.08524. [arXiv ] [doi.org ]
“Abelian surfaces good away from ,” with Akio Tamagawa, International Journal of Number Theory 13 (2017), no. 4, pp. 991-1001 (2017). [arXiv ] [doi.org ]
“Arithmetic of abelian varieties with constrained torsion ,” with Akio Tamagawa, Transactions of the American Mathematical Society 369 (2017), no. 4, pp. 2395-2424. arXiv:1302.1477. [ arXiv ] [doi.org ] “Picard curves over ,” with Beth Malmskog, LMS Journal of Computation and Mathematics , 19 (2016), no. 2, pp. 382-408. arXiv: 1407.7892. [arXiv ] [doi.org ]
“Character sums determined by low degree isogenies of elliptic curves ,” with Dustin Moody, Rocky Mountain Journal of Mathematics 45 (2015), no. 2, pp. 623-635. arXiv:1210.2743. [ arXiv ] [doi.org ] “Class number formulas via ,” with Cam McLeman, Bulletin of the London Mathematical Society 44 (2012), no. 6, pp. 1221-1236. [arXiv ] [doi.org ] “An abelian surface with constrained ,” in Advanced Studies in Pure Mathematics 63: Galois-Teichmüller Theory and Arithmetic Geometry , Hiroaki Nakamura, Florian Pop, Leila Schneps, Akio Tamagawa (eds), Mathematical Society of Japan, Tokyo, 2012, pp. 449-456. [doi.org ]
“On elliptic curves of conductor ,” Algebraic number theory and related topics 2007 , RIMS Kôkyûroku Bessatsu, B12, Res. Inst. Math. Sci. (RIMS), Kyoto, 2009, pp. 101-113. [Journal proof ] “A finiteness conjecture on abelian varieties with constrained prime power torsion ,” Mathematical Research Letters 15 (2008), no. 6, pp. 1223-1231. [doi.org ]“On the torsion of Jacobians of principal modular curves of level ,” with Matthew Papanikolas, Archiv der Mathematik (Basel) 88 (2007), no. 1, pp. 19-28. [ arXiv ] [doi.org ] “On the fields of ,” Mathematical Research Letters 11 (2004), no. 4, pp. 529-538. [doi.org ]
-unit equation and several applications,” with Alejandra Alvarado, Angelos Koutsianas, Beth Malmskog, Christelle Vincent, Mckenzie West. In: Balakrishnan, J.S., Elkies, N., Hassett, B., Poonen, B., Sutherland, A.V., Voight, J. (Des) Arithmetic Geometry, Number Theory, and Computation. Simons Symposia. Springer, Cham, 2021, pp. 1-41. arXiv:1903.00977. [arXiv] [doi.org]
,” with Akio Tamagawa, International Journal of Number Theory 13 (2017), no. 4, pp. 991-1001 (2017). [arXiv] [doi.org]
with good reduction away from
,” with Beth Malmskog, LMS Journal of Computation and Mathematics, 19 (2016), no. 2, pp. 382-408. arXiv: 1407.7892. [arXiv] [doi.org]
and an open question of Ihara,” Algebraic number theory and related topics 2007, RIMS Kôkyûroku Bessatsu, B12, Res. Inst. Math. Sci. (RIMS), Kyoto, 2009, pp. 101-113. [Journal proof]
,” with Matthew Papanikolas, Archiv der Mathematik (Basel) 88 (2007), no. 1, pp. 19-28. [arXiv] [doi.org]