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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.

accepted for publication in the American J. of Mathematics

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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

accepted for publication in the J. Australian Math. Soc.

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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.

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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„“)

(May 2023). Forum Mathematicum: revisions

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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

(August 2023).

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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,

(September 2023), with Aditya Karnataki

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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 metabelian extensions,

(Jan 2024) with Siddhi Pathak

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53. On Malle's conjecture for the product of symmetric and nilpotent groups,

with Hrishabh Mishra

Nagoya Math. J : revisions

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54. An analogue of Kida's formula for elliptic curves with additive reduction

with Pratiksha Shingavekar,

accepted for publication in the The Ramanujan Journal

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55. Rank distribution in cubic twist families of elliptic curves

(Mar 2024) with Pratiksha Shingavekar

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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 : revisions

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58. Hilbert's tenth problem for families of â„¤p-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,

(June 2024)

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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 â„¤p-extension, (Sep 2024)