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1. Constructing Certain Special Analytic Galois Extensions
J. Number theory (2020) Vol. 212, pp. 105-112 (journal version).
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2. Euler Characteristics and their Congruences in the Positive Rank setting
with Ramdorai Sujatha,
Canadian Math. Bull. (2021) Vol. 64, no. 1, pp. 228-245 (journal version).
3. On Picard Groups of Perfectoid Covers of Toric varieties
with Gabriel Dorfsman-Hopkins and Peter Wear,
European J. of Mathematics (2023) Vol. 9, issue 1, article 16. (journal version).
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4. Euler Characteristics and their Congruences for Multi-signed Selmer groups
with Ramdorai Sujatha,
Canadian J. of Mathematics (2023) Vol. 75(1), pp. 298-321.(journal version).
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5. A Refined Lifting Theorem for Supersingular Galois Representations
J. Number theory (2021) Vol. 229, pp. 282-313 (journal version).
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6. Constructing Galois Representations Ramified at One Prime
J. Number theory (2021) Vol. 222, pp. 168-180 (journal version).
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7. Deformations of Certain Reducible Galois Representations III
Int. J. Number theory (2021) Vol. 17, Issue 06 pp. 1429-1485 (journal version).
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8. Anticyclotomic μ-invariants of residually reducible Galois Representations
with Debanjana Kundu,
J. Number theory (2022) Vol. 234, pp. 476-498 (journal version).
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9. Iwasawa Invariants for Elliptic Curves over Zp-extensions and Kida's formula
with Debanjana Kundu.
Forum Mathematicum. 34 (2022), no. 4, 945–967 (journal version, Link to auxiliary code).
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10. Deformations of Reducible Galois Representations to Hida Families
Int. J. Number theory (2022) Vol. 18, No. 01, pp. 89-112 (journal version).
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11. On the μ-invariants of residually reducible Galois representations
with Ramdorai Sujatha.
American J. of Mathematics (2024) Vol.146, No. 6, pp. 1617-1649 (journal version)
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12. Constructing Galois Representations with large Iwasawa λ-invariant
Annales Math. Quebec 48 (2024), no. 1, 253–268. (journal version)
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13. Statistics for Iwasawa Invariants of Elliptic Curves
with Debanjana Kundu,
Trans. American Math. Soc. (2021) Vol. 374, no.11, pp. 7945-7965 (journal version).
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14. Statistics for Anticyclotomic Iwasawa Invariants of Elliptic Curves
with Jeffrey Hatley and Debanjana Kundu.
Math Zeitschrift : (2024), Vol 307, no. 3, Paper No. 49. (journal version)
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15. Statistics for Iwasawa Invariants of Elliptic Curves, II
with Debanjana Kundu.
Int. J. Number theory Volume 20, Issue 04 (May 2024), pp.1099-1124 (journal version)
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16. Rank Jumps and Growth of Shafarevich-Tate groups of Elliptic curves in Z/pZ-extensions; with Lea Beneish and Debanjana Kundu.
J. Australian Math. Soc. 116 (2024), no. 1, 1–38. (journal version)
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17. Arithmetic Statistics for Galois Deformation Rings
with Tom Weston.
The Ramanujan Journal (2024), no. 3, pp. 685-708 (journal version)
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18. Arithmetic Statistics and Diophantine Stability for Elliptic curves
The Ramanujan Journal (2023), 62, pp. 215–239 (journal version)
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19. Asymptotic Growth for Mordell-Weil Ranks of Elliptic curves in Noncommutative Towers
Canadian Math. Bull. (2022), 65(4), pp. 1050-1062. (journal version).
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20. Arithmetic Statistics and Noncommutative Iwasawa theory
with Debanjana Kundu and Antonio Lei
Documenta Math. (2022), 27, pp. 89-149 (journal version).
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21. Rational points on Algebraic Curves in Infinite towers of Number fields
The Ramanujan Journal (2023), Vol. 60, pp. 809–824. (journal version).
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22. Statistics for p-ranks of Artin-Schreier covers
Acta Arithmetica 205 (2022) , 211-226 (journal version).
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23. Iwasawa Invariants for Symmetric Square representations
with Ramdorai Sujatha and Vinayak Vatsal
Research in the Mathematical Sciences (2023), Vol 10, issue 1, 27. (journal version)
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24. Arithmetic Statistics for the Fine Selmer group in Iwasawa theory
with Ramdorai Sujatha
Research in Number theory (2023), Vol 9, issue 3, 59. (journal version)
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25. On the μ equals zero conjecture for the Fine Selmer group in Iwasawa theory
with Shaunak Deo and Ramdorai Sujatha
Pure & Applied Math. Quarterly (2023) vol.19, no.2, pp. 641-680 (journal version)
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26. Topological Iwasawa invariants and Arithmetic Statistics
with Cedric Dion
Documenta Math. (2022), 27, pp. 1643-1669 (journal version).
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27. Class group statistics for torsion fields generated by elliptic curves
with Tom Weston
J. Australian Math. Soc. (2025), Vol. 118, No. 2, pp. 245-264 (journal version).
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28. Asymptotic growth of Iwasawa invariants in Noncommutative towers of number fields
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29. Remarks of Hilbert's tenth problem and the Iwasawa theory of elliptic curves
Bull. Australian Math. Soc. (2023), 107(3), pp. 440-450 (journal version)
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30. Remarks on Catalan's equation over Function fields
Finite Fields & their Applications (2023), Vol. 91, no. 102271 (journal version)
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31. Diophantine equations of the form Y^n=f(X) over function fields
Bull. Australian Math. Soc. 108 (2023), no. 3, pp. 379–390. (journal version)
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32. On the distribution of Iwasawa invariants associated to Multigraphs
with Cedric Dion, Antonio Lei and Daniel Vallieres.
Nagoya Math. J. 108, Volume 253, (2024) , pp. 48 - 90 (journal version)
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33. A note on the distribution of Iwasawa invariants of imaginary quadratic fields
Bull Braz Math Soc (2023), New Series 54, 36. (journal version)
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34. On large Iwasawa λ-invariants of imaginary quadratic function fields
The Ramanujan Journal (2023), Vol. 62, pp. 853-861 (journal version)
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35. On the corank of the fine Selmer group of an elliptic curve over a Zp-extension
The Ramanujan Journal Vol. 62 (2023), no. 4, 1023–1035.(journal version)
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36. An analogue of Kida's formula in graph theory
with Daniel Vallieres
accepted for publication in Pure & Applied Math. Quarterly
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37. Galois representations ramified at one prime and with suitably large image
Trans. American Math. Soc. (2023) Vol. 376 No.10, pp. 7287-7305 (journal version)
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38. On the number of subrings of Z^n of prime power index
with Hrishabh Mishra
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39. On the distribution of Alexander polynomials in certain families of closed braids
European J. of Mathematics (2023) Vol 9, Issue 3, article 65 (journal version)
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40. Hilbert's tenth problem in anticyclotomic towers of number fields
with Tom Weston
Trans. American Math. Soc. (2024) Vol. 377, No. 5, pp. 3577-3597 (journal version)
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41. Constructing Galois representations with prescribed Iwasawa λ-invariant
Bulletin of the London Math. Soc. (2024) Vol. 56, Issue. 5, pp. 1624-1642 (journal version)
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42. On the distribution of eigenvalues in families of Cayley graphs
with Matilde Lalin
European J. of Mathematics (2024) Vol.10, number 49 (journal version)
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43. Diophantine stability for elliptic curves on average
(April 2023) with Tom Weston
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44. Lower bounds for the number of number fields with Galois group GL2(Fâ„“)
Forum Mathematicum, vol. 37, no. 5, 2025, pp. 1589-1596 (journal version)
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45. Counting number fields whose Galois group is a wreath product of symmetric groups
(June 2023) with Hrishabh Mishra
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46. Remarks on Greenberg's conjecture for Galois representations associated to elliptic curves
accepted for publication in Journal of the Korean Math Soc.
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47. Asymptotic growth patterns for class field towers ,
with Arindam Bhattacharyya and Vishnu Kadiri,
Documenta Math. 29 (2024), no. 1, 141–158 (journal version).
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48. On the Iwasawa invariants of Artin representations,
with Aditya Karnataki,
Research in Number theory (2025), Vol 11, issue 2, 47. (journal version)
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49. Upper bounds on the number of number fields with prescribed Galois group
(October 2023) with Hrishabh Mishra
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50. Iwasawa theory of fine Selmer groups associated to Drinfeld modules
Mathematika (2024) Volume70, Issue3 (journal version)
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51. The T-adic Galois representation is surjective for a positive density of Drinfeld modules; Research in Number theory: Vol 10, No. 56 (2024) (journal version)
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52. Rank stability of elliptic curves in certain non-abelian extensions,
with Siddhi Pathak
Math Nachrichten 298 (2025), pp.730-753 (journal version)
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53. On Malle's conjecture for the product of symmetric and nilpotent groups,
with Hrishabh Mishra
accepted for publication in Nagoya Math. J
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54. An analogue of Kida's formula for elliptic curves with additive reduction
with Pratiksha Shingavekar,
The Ramanujan Journal Vol. 65 (2024), no. 2, pp. 857–883 (journal version)
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55. Rank distribution in cubic twist families of elliptic curves
Acta Arithmetica Vol. 219 (2025), no. 3, pp. 249–273 (journal version)
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56.Statistics for Iwasawa Invariants of Elliptic Curves, III
(Apr 2024)
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57.On the Iwasawa theory of Cayley graphs
(May 2024) with Sohan Ghosh,
Research in the Mathematical Sciences (2025) Vol. 12 No. 2 (journal version)
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58. Hilbert's tenth problem for families of ℤp-extensions of imaginary quadratic fields
(June 2024) with Katharina Müller
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59.Galois representations over function fields that are ramified at one prime,
The Ramanujan Journal Vol. 66, no. 30 (2025) (journal version)
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60. A positive density of elliptic curves are diophantine stable in certain Galois extensions,
(June 2024) with Pratiksha Shingavekar
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61.Galois representations are surjective for almost all Drinfeld modules,
(July 2024)
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62.Counting rational maps on â„™^1 with prescribed local conditions,
(Aug 2024) with Khoa D. Nguyen
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63. A heuristic approach to the Iwasawa theory of elliptic curves,
(Sep 2024) with Katharina Müller
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64. Integers that are sums of two cubes in the cyclotomic ℤp-extension, (Sep 2024)
accepted for publication in the Tohoku Math J.
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65. Iwasawa theory and ranks of elliptic curves in quadratic twist families (Dec 2024)
with Jeffrey Hatley​
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66. Diophantine approximation and the subspace theorem (Feb 2025)
with Shivani Goel and Rashi Lunia
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67. Iwasawa theory and the representations of finite groups (April 2025)
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68. Selmer stability for elliptic curves in Galois â„“-extensions (April 2025)
with Siddhi Pathak
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69. Deformations of reducible Galois representations with large Selmer p-rank (April 2025)
with Eknath Ghate
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70. Selmer stability in families of congruent Galois representations (May 2025)
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71. The second moment of cubic Dirichlet L-functions over function fields (May 2025) with Shivani Goel
