Research papers:

Preprints/Submitted for Publication:

• [68] On the stratification conjecture for CM torsion subgroups (pdf)
• [67] Functional degrees and arithmetic applications II: the group-theoretic prime Ax-Katz therem (with U. Schauz). (pdf)
• [66] CM elliptic curves: volcanoes, reality and applications, Part II (with F. Saia) (pdf)
• [65] CM elliptic curves: volcanoes, reality and applications, Part I (pdf)
• [64] A Mean Value Inequality for all functions (pdf)
• [63] Restricted Variable Chevalley-Warning Theorems (with A. Bishnoi) (pdf)
• [62] On base size sets (pdf)
• [61] Solution to the inverse Mordell-Weil problem for elliptic curves (pdf)
• [60] Abstract geometry of numbers: linear forms. (pdf)
• [59] Curves over global fields violating the Hasse Principle. (pdf).
• [58] Period-index problems in WC-groups II: abelian varieties. (pdf)

Accepted and/or Published:

• [57] Functional degrees and airthmetic applications III: beyond prime exponent. (with U. Schauz). To appear, Math. Proc. Cambridge Phil. Soc. (pdf)
• [56] Ax's lemma in the Aichinger-Moosbauer calculus (with N. Triantafillou). J. Algebra 659 (2024), 542-580. (pdf)
• [55] Densities of integer sets represented by quadratic forms (with P. Pollack, J. Rouse and K. Thompson). J. Number Theory 256 (2024), 290-328. (pdf)
• [54] Functional degrees and arithmetic applications I: the set of functional degrees. (with U. Schauz) J. Algebra 608 (2022), 691-718. (pdf)
• [53] The least degree of a CM point on a modular curve (with T. Genao, P. Pollack and F. Saia) J. Lond. Math. Soc. (2) 105 (2022), 825-883. (pdf)
• [52] Chevalley-Warning at the boundary (with T. Genao and F. Saia) Expo. Math. 39 (2021), no. 4, 604-623. (pdf)
• [51] Acyclotomy of torsion in the CM case (with M. Chou and M. Milosevic) Ramanujan J. 55 (2021), no. 3, 1015-1037. (pdf)
• [50] Torsion points and isogenies on CM elliptic curves (with A. Bourdon) J. Lond. Math. Soc. (2) 102 (2020), 580-622. (pdf)
• [49] Torsion points and Galois representations on CM elliptic curves (with A. Bourdon) Pacific J. Math. 305 (2020), 43-88. (pdf)
• [48] Reciprocity by resultant in k[t] (with P. Pollack) Enseign. Math. 65 (2019), 101-116. (pdf)
• [47] The Instructor's Guide to Real Induction Math. Mag. 92 (2019), 136-150. (pdf)
• [46] Rabinowitsch times six Rocky Mountain J. Math. 49 (2019), 433-485. (pdf)
• [45] Warning's Second Theorem with relaxed outputs J. Algebraic Combin. 48 (2018), 325-349. (pdf)
• [44] ABC and the Hasse principle for quadratic twists of hyperelliptic curves (with L.D. Watson) C. R. Math. Acad. Sci. Paris 356 (2018), 911-915. (pdf)
• [43] Typically bounding torsion (with M. Milosevic and P. Pollack) J. Number Theory 192 (2018), 150-167. (pdf)
• [42] Varga's theorem in number fields (with L.D. Watson) INTEGERS 18 (2018), A74, 11 pp. (pdf)
• [41] A generalization of the theorems of Chevalley-Warning and Ax-Katz via polynomial substitutions. (with I.N. Baoulina and A. Bishnoi) Proc. Amer. Math. Soc. 147 (2019), 4107-4122. (arxiv preprint)
• [40] A Note on Golomb topologies (with N. Lebowitz-Lockard and P. Pollack) Quaest. Math. 42 (2019), 73-86. (pdf)
• [39] There are genus one curves of every index over every infinite, finitely generated field (with A. Lacy). J. Reine Angew. Math. 749 (2019), 65-86. (pdf)
• [38] Hasse Principle Violations for Atkin-Lehner Twists of Shimura Curves (with J. Stankewicz) Proc. Amer. Math. Soc. 146 (2018), 2839-2851. (pdf)
• [37] Pursuing polynomial bounds on torsion (with P. Pollack) Israel J. Math. 227 (2018), 889-909. (pdf)
• [36] A note on rings of finite rank Comm. Algebra 46 (2018), 4223-4232. (pdf)
• [35] The truth about torsion in the CM case, II (with P. Pollack) Q. J. Math. 68 (2017), 1313-1333. (pdf)
• [34] The number of atoms in a primefree atomic domain (with S. Gosavi and P. Pollack). Comm. Algebra 45 (2017), 5431-5442. (pdf)
• [33] On zeros of a polynomial in a finite grid (with A. Bishnoi, A. Potukuchi and J.R. Schmitt). Combin. Probab. Comput. 27 (2018), no. 3, 310-333. (pdf).
• [32] Algebraic curves uniformized by congruence subgroups of triangle groups (with J. Voight). Trans. Amer. Math. Soc. 371 (2019), 33-82. (pdf)
• [31] The cardinal Krull dimension of a ring of holomorphic functions. Expo. Math. 35 (2017), 350-356. (pdf)
• [30] Anatomy of torsion in the CM case (with A. Bourdon and P. Pollack) Math. Z. 285 (2017), no. 795-820. (pdf)
• [29] The Euclidean criterion for irreducibles. Amer. Math. Monthly 124 (2017), 198-216. (pdf)
• [28] Torsion points on CM elliptic curves over real number fields (with A. Bourdon and J. Stankewicz). Trans. Amer. Math. Soc. 369 (2017), 8457-8496. (pdf)
• [27] The truth about torsion in the CM case (with P. Pollack). C. R. Math. Acad. Sci. Paris 353 (2015), 683-688. (pdf)
• [26] Warning's second theorem with restricted variables (with A. Forrow and J. Schmitt). Combinatorica 37 (2017), 397-417. (pdf)
• [25] A Note on Euclidean order types. Order 32 (2015), 157-178. (pdf)
• [24] Extending the Zolotarev-Frobenius approach to quadratic reciprocity (with A. Brunyate). Ramanujan J. 37 (2015), 25-50. (pdf)
• [23] The Combinatorial Nullstellensätze revisited. Electronic Journal of Combinatorics. Volume 21, Issue 4 (2014). Paper #P4.15 (pdf)
• [22] Computation on elliptic curves with complex multiplication (with P. Corn, A. Rice and J. Stankewicz). LMS Journal of Computation and Mathematics 17 (2014), 509-535. (link to the arxiv)
• [21] Euclidean quadratic forms and ADC-Forms II: integral forms (with W. Jagy). Acta Arithmetica 164 (2014), 265-308. (pdf)
• [20] Absolute convergence in ordered fields. (with N.J. Diepeveen). American Math. Monthly 121 (2014), 909-916. (pdf)
• [19] Graph derangements. Open Journal of Discrete Mathematics 3 (2013), 183-191. (link to the arxiv)
• [18] GoNI: Primes represented by binary quadratic forms) (with J. Hicks, H. Parshall and K. Thompson). INTEGERS 13 (2013), A37, 18pp. (pdf)
• [17] Torsion points on elliptic curves with complex multiplication (with an appendix by Alex Rice) (with B. Cook and J. Stankewicz). International Journal of Number Theory 9 (2013), 447-479. (pdf)
• [16] GoNII: Universal quaternary quadratic forms (with J. Hicks, K. Thompson and N. Walters). INTEGERS 12 (2012), A50, 16 pp. (pdf)
• [15D] Euclidean quadratic forms are ADC forms: a short proof (by F. Dacar (only!)). (pdf)
• [15] Euclidean quadratic forms and ADC forms I, Acta Arithmetica 154 (2012), 137-159. (pdf)
  
• [14] Covering numbers in linear algebra, American Math. Monthly 119 (2012), 65-67. (pdf)
  
• [13] Period-index problems in WC-groups IV: a local transition theorem, J. Théor. Nombres Bordeaux 18 (2010), 583-606.(pdf)
• [12] Period, index and potential Sha (with S. Sharif), Algebra Number Theory 4 (2010), 151-174. (pdf)
• [11] Elliptic Dedekind domains revisited. Enseignement Math. 55 (2009), 213-225. (pdf)
• [10] On the Hasse principle for Shimura curves, Israel J. Math. 171 (2009), no. 1, 349-365. (pdf)
• [9] An ''Anti-Hasse Principle'' for prime twists. Int. J. of Number Theory 4 (2008), 627-637. (pdf)
• [8] Local bounds for torsion points on abelian varieties (with X. Xarles). Canad. J. Math. 60 (2008), 532-555. (pdf)
• [7] Abelian points on algebraic varieties. Math. Res. Lett. 14 (2007), 731-743. (pdf)
• [6] On the indices of curves over local fields. Manuscripta Math. 124 (2007), 411-426. (pdf)
• [5] Galois groups via Atkin-Lehner twists. Proc. Amer. Math. Soc. 135 (2007), 617-624. (pdf)
• [4] There are genus one curves of every index over every number field. J. Reine Angew. Math. 594 (2006), 201-206. (pdf)
• [3] On elementary equivalence, isogeny and isomorphism. J. Théor. Nombres Bordeaux 18 (2006), no. 1, 29-58. (pdf)
• [2] On the Number of Representations of an Integer by a Linear Form (with G. Alon). Journal of Integer Sequences, Vol. 8 (2005), Article 05.5.2 (free online publication)
• [1] Period-index problems in WC-groups I: elliptic curves. J. Number Theory 114 (2005), 193-208. (pdf)