Publications

Preprints

  • Lei A, Mueller K, “On Zp-towers of graph coverings arising from a constant voltage assignment”,
  • Lei A, Pollack R, Pratap N, “Asymptotic formulae for Iwasawa Invariants of Mazur–Tate elements of elliptic curves”
  • Lei A, Mastella L, Zhao L, “On the structure of the Bloch–Kato Selmer groups of modular forms over anticyclotomic Zp-towers”
  • Isik E, Lei A, “The growth of Tate-Shafarevich groups of p-supersingular elliptic curves over anticyclotomic Zp-extensions at inert primes”
  • Lei A, “Artin formalism for p-adic L-functions of modular forms at non-ordinary primes”
  • Burungale A, Buyukboduk K, Lei A, “Anticyclotomic Iwasawa theory of abelian varieties of GL2-type at non-ordinary primes II”

Articles accepted for publication

  • Kundu D, Lei A, “Mazur’s growth number conjecture in the rank one case”, The Quarterly Journal of Mathematics
  • Lei A, Mueller K, “Isogeny graphs with level structures arising from the Verschiebung map”, the proceedings of the ICTS program “Elliptic curves and the special values of L-functions”
  • Gajek-Leonard R, Hatley J, Kundu D, Lei A, “On a conjecture of Mazur predicting the growth of Mordell–Weil ranks in Zp-extensions”, Mathematical Research Letters
  • Buyukboduk K, Lei A, “Iwasawa theory of twists of elliptic modular forms over imaginary quadratic fields at inert primes”, Mémoires de la société mathématique de France

Published Articles

  1. Kundu D, Lei A, “Non-vanishing modulo p of Hecke L-values over imaginary quadratic fields”, Israel Journal of Mathematics, Volume 266, pages 307–339, (2025)
  2. Balakrishnan S S, Lei A, Palvannan B “On computing the Newton polygons of plus and minus p-adic L-functions”, Involve – a Journal of Mathematics, Vol. 18 (2025), No. 3, 401–416
  3. Lei A, Mueller K, “On towers of isogeny graphs with full level structure”, Research in Mathematical Sciences, Volume 12, article number 4, (2025)
  4. Kundu D, Lei A, Sprung F, “Studying Hilbert’s 10th problem via explicit elliptic curves”, Mathematische Annalen, Volumne 390, 2024, 5153-5183 
  5. Lei A, Mueller K, “On ordinary isogeny graphs with level structure”, Expositiones Mathematicae, Volume 42, Issue 5, 2024, 125589  
  6. Doyon A, Lei A “Lambda-invariants of Mazur–Tate elements attached to Ramanujan’s tau function and congruences with Eisenstein series”, Research in Number Theory, Volume 10, article number 53, (2024)
  7. Dion C, Lei A, Ray A, Vallières D, “On the distribution of Iwasawa invariants associated to multigraphs”, Nagoya Mathematical Journal, Volume 253 , 2024 , 48 – 90
  8. Lei A, Zhao L, “On the BDP Iwasawa main conjecture for modular forms”, Manuscripta Mathematica, Volume 173, pages 867–888, (2024)
  9. Lei A, Mueller K, “On the zeta functions of supersingular isogeny graphs and modular curves”, Archiv der Mathematik, Volume 122, pages 285–294, (2024)  
  10. Burungale A, Buyukboduk K, Lei A, “Anticyclotomic Iwasawa theory of abelian varieties of GL2-type at non-ordinary primes”, Advances in Mathematics, Volume 439, March 2024, 109465
  11. Lei A, Mueller K, Xia J, “On the Iwasawa invariants of BDP Selmer groups and BDP p-adic L-functions”, Forum Mathematicum, 36 (1) 2024, 153-172.   
  12. Lei A, “A remark on the characteristic elements of anticyclotomic Selmer groups of elliptic curves with complex multiplication at supersingular primes”, The Quarterly Journal of Mathematics, 74 (4), 2023, 1435–1487
  13. Lei A, Lim M F, Mueller K, “Asymptotic formula for Tate-Shafarevich groups of p-supersingular elliptic curves over anticyclotomic extensions”, Advances in Mathematics, volume 434, Article number: 109320 (2023)
  14. Kundu D, Lei A, “Growth of p-parts of ideal class groups and fine Selmer groups in Zq-extensions with p≠q”, Acta Arithmetica, 207 (2023), 297-313
  15. Lei A, Vallières D, “The non-ℓ-part of the number of spanning trees in abelian ℓ-towers of multigraphs”, Research in Number Theory, 9, 18 (2023)
  16. Hatley J, Lei A, “The vanishing of anticyclotomic mu-invariants for non-ordinary modular forms “, Comptes Rendus Mathématique, 361 (2023), 65-72
  17. Hatley J, Kundu D, Lei A, Ray J, “Control theorems for fine Selmer groups, and duality of fine Selmer groups attached to modular forms”, the Ramanujan Journal, 60, 237–258 (2023)
  18. Lei A, “Algebraic structure and characteristic ideals of fine Mordell–Weil groups and plus/minus Mordell–Weil groups”, Mathematische Zeitschrift, volume 303, Article number: 14 (2023)
  19. Lei A, Ray J, “Iwasawa theory of automorphic representations of GL2n at non-ordinary primes”, Research in Mathematical Sciences, 10, 1, 2023
  20. Buyukboduk K, Lei A, “Iwasawa theory for GL2×ResK/QGL1“, Annales mathématiques du Québec (special volume in honour of Bernadette Perrin-Riou), 46 (2), 2022, 347-418
  21. Lei A, Palvannan B, “Codimension two cycles in Iwasawa theory and tensor product of Hida families”, Mathematische Annalen, 383, no.1-2, 2022, 39–75
  22. Cauchi A, Lei A “On the analogue of Mazur-Tate type conjectures in the Rankin-Selberg setting”, 66 (2), 2022, 571-630, Publicacions Matemàtiques
  23. Doyon A, Lei A “Congruences between Ramanujan’s tau function and elliptic curves, and Mazur–Tate elements at additive primes”, The Ramanujan Journal, 58, 2022, 505–522
  24. Lei A, Lim M F, ” On fine Selmer groups and signed Selmer groups of elliptic modular forms”, Bulletin of the Australian Mathematical Society, 105 (3), 2022, 419 – 430
  25. Kundu D, Lei A, Ray A, “Arithmetic Statistics and noncommutative Iwasawa Theory”, Documenta Mathematica, 27, 2022, 89-149
  26. Lei A, Lim M F, “Mordell-Weil ranks and Tate-Shafarevich groups of elliptic curves with mixed-reduction type over cyclotomic extensions”, International Journal of Number Theory, 18 (2), 2022, 303-330
  27. Hatley J, Lei A, Vigni S, “Λ-submodules of finite index of anticyclotomic plus and minus Selmer groups of elliptic curves”, Manuscripta Mathematica, 167, 2022, 589-612
  28. Lei A, Lim M F, “Akashi series and Euler characteristics of signed Selmer groups of elliptic curves with semistable reduction at primes above p”, Journal de théorie des nombres de Bordeaux (proceeding of Iwasawa 2019), 33 (3.2), 2021, 997-1019
  29. Buyukboduk K, Lei A, “Interpolation of Generalized Heegner Cycles in Coleman Families”, Journal of London Mathematical Society, 104 (4), 2021, 1682-1716
  30. Buyukboduk K, Lei A, “Iwasawa theory of elliptic modular forms over imaginary quadratic fields at non-ordinary primes”, International Mathematics Research Notices,  2021 (14), 2021, 10654–10730  
  31. Hatley J, Lei A, “Comparing anticyclotomic Selmer groups of positive coranks for congruent modular forms — Part II”, Journal of Number Theory, 229, 2021, 342–363
  32. Lei A, Sujatha R, “On fine Selmer groups and the greatest common divisor of signed and chromatic p-adic L-functions”, Proceedings of the American Mathematical Society, 149 (8), 2021, 3235–3243
  33. Buyukboduk K, Lei A, Venkat G, “Iwasawa theory for symmetric square of non-p-ordinary eigenforms”, Documenta Mathematica, 26, 2021, 1–63
  34. Lei A, Sujatha R, “On Selmer groups in the supersingular reduction case”, Tokyo Journal of Mathematics, 43 (2), 2020, 455–479
  35. Bellemare H, Lei A, “Explicit uniformizers for certain totally ramified extensions of the field of p-adic numbers”, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 90 (1), 2020, 73–83
  36. Lei A, Poulin A, “On certain probabilistic properties of polynomials over the ring of p-adic integers”, American Mathematical Monthly, 127 (6), 2020, 519–529
  37. Delbourgo D, Lei A, “Heegner cycles and congruences between anticyclotomic p-adic L-functions over CM-extensions”, The New York Journal of Mathematics, 26, 2020, 496–525
  38. Lei A, Sprung F, “Ranks of elliptic curves over Z_p^2-extensions”, Israel Journal of Mathematics, 236 (1), 2020, 183–206  
  39. Buyukboduk K, Lei A, “Functional Equation for p-adic Rankin-Selberg L-functions”, Annales mathématiques du Québec, 44 (1), 2020, 9–25  
  40. Lei A, Ponsinet G, “On the Mordell-Weil ranks of supersingular abelian varieties in cyclotomic extensions”, Proceedings of the American Mathematical Society Series B, 7, 2020, 1-16
  41. Buyukboduk K, Lei A, “Rank–two Euler systems for symmetric squares”, Transactions of the American Mathematical Society,  372 (12), 2019, 8605-8619  
  42. Hatley J, Lei A, “Comparing anticyclotomic Selmer groups of positive coranks for congruent modular forms”, Mathematical Research Letters, 26 (4), 2019, 1115-1144  
  43. Lei A, Palvannan B, “Codimension two cycles in Iwasawa theory and elliptic curves with supersingular reduction”, Forum of Mathematics, Sigma, 7, 2019, e25  
  44. Hatley J, Lei A, “Arithmetic properties of signed Selmer groups at non-ordinary primes”, Annales de l’Institut Fourier, 69 (3) 2019, 1259-1294  
  45. Buyukboduk K, Lei A, Loeffler D, Venkat G, “Iwasawa theory for Rankin–Selberg products of p-non-ordinary eigenforms”, Algebra & Number Theory, 13(4), 2019, 901-941  
  46. Lei A, Loeffler D, Zerbes S, “Euler systems for Hilbert modular surfaces”, Forum of Mathematics, Sigma, 6, 2018 , e23  
  47. Delbourgo D, Lei A, “Congruences modulo p between rho-twisted Hasse-Weil L-values”, Transactions of the American Mathematical Society, 370 (11), 2018, 8047-8080   
  48. Buyukboduk K, Lei A, “Anticyclotomic p-ordinary Iwasawa theory of elliptic modular forms”, Forum Mathematicum, 30 (4), 2018, 887–913  
  49. Lei A, “Bounds on the Tamagawa numbers of a crystalline representation over towers of cyclotomic extensions”, Tohoku Mathematical Journal, 69 (4), 2017, 497-524  
  50. Dion, C, Lei, A “Plus and minus logarithms and Amice transform”, Comptes Rendus Mathématique, 355 (9), 2017, 942-948  
  51. Lei A, “Estimating class numbers over metabelian extensions”, Acta Arithmetica, 180 (4), 2017, 347-364  
  52. Lei A, Loeffler D, Zerbes S, “On the asymptotic growth of Bloch-Kato-Shafarevich-Tate groups of modular forms over cyclotomic extensions”, Canadian Journal of Mathematics, 69 (4), 2017, 826-850  
  53. Buyukboduk K, Lei A, “Integral Iwasawa Theory of Galois Representations for non-ordinary primes”, Mathematische Zeitschrift, 286 (1), 2017, 361-398  
  54. Lei A, Ponsinet G, “Functional equations for multi-signed Selmer groups”, Annales mathématiques du Québec, 41 (1), 2017, 155-167  
  55. Delbourgo D, Lei A, “Estimating the growth in Mordell-Weil ranks and Shafarevich-Tate groups over Lie extensions”, The Ramanujan Journal, 43 (1), 2017, 29-68  
  56. Ayotte D, Lei A, Rondy-Turcotte J-C, “On the parity of supersingular Weil polynomials”, Archiv der Mathematik, 106 (4), 2016, 345-353  
  57. Delbourgo D, Lei A, “Non-commutative Iwasawa theory for elliptic curves with multiplicative reduction”, Mathematical Proceedings of the Cambridge Philosophical Society, 160 (1), 2016, 11-38  http://dx.doi.org/10.1017/S0305004115000535
  58. Buyukboduk K, Lei A, “Coleman-adapted Rubin-Stark Kolyvagin systems and supersingular Iwasawa theory of CM abelian varieties”, Proceedings of the London Mathematical Society, 111 (6), 2015, 1338-1378  http://dx.doi.org/10.1112/plms/pdv054
  59. Delbourgo D, Lei A, “Transition formulae for ranks of abelian varieties”, Rocky Mountain Journal of Mathematics, 45 (6), 2015, 1807-1838  http://projecteuclid.org/euclid.rmjm/1411945718
  60. Lei A, Loeffler D, Zerbes S, “Euler systems for modular forms over imaginary quadratic fields”, Compositio Mathematica, 151 (9), 2015, 1585-1625  http://dx.doi.org/10.1112/S0010437X14008033
  61. Harron R, Lei A, “Iwasawa theory for symmetric powers of CM modular forms at non-ordinary primes”, Journal de théorie des nombres de Bordeaux, 26(3), 2014, 673-707  
  62. Lei A, “Factorisation of two-variable p-adic L-functions”, Canadian Mathematical Bulletin, 57(4), 2014, 845-852  http://dx.doi.org/10.4153/CMB-2013-044-2
  63. Lei A, Loeffler D, Zerbes S, “Euler systems for Rankin-Selberg convolutions of modular forms”, Annals of Mathematics, 180(2), 2014, 653-771  https://doi.org/10.4007/annals.2014.180.2.6
  64. Lei A, Loeffler D, Zerbes S, “Critical Slope p-adic L-functions of CM Modular Forms”, Israel Journal of Mathematics, 198(1), 2013, 261-282  
  65. Lei A, “Non-commutative p-adic L-functions for Supersingular Primes”, International Journal of Number Theory, 8(8), 2012, 1813-1830  
  66. Lei A, Zerbes S, “Signed Selmer Groups over p-adic Lie Extensions”, Journal de théorie des nombres de Bordeaux, 24(2), 2012, 377-403  
  67. Lei A, “Iwasawa Theory for the Symmetric Square of a CM Modular Forms at Inert Primes”, Glasgow Mathematical Journal, 54(2), 2012, 241-259  
  68. Lei A, Loeffler D, Zerbes S, “Coleman Maps and p-adic Regulator”, Algebra and Number Theory, 5(8), 2011, 1095-1131  
  69. Lei A, “Iwasawa Theory for Modular Forms at Supersingular Primes”, Compositio Mathematica, 147(3), 2011, 803-838 acroread 
  70. Lei A, Loeffler D, Zerbes S, “Wach Modules and Iwasawa Theory for Modular Forms”, Asian Journal of Mathematics, 14(4), 2010, 475-528  
  71. Lei A, “Coleman Maps for Modular Forms at Supersingular Primes over Lubin-Tate Extensions”, Journal of Number Theory, 130(10), 2010, 2293-2307  

Other articles

  • Lei A, “Iwasawa Theory for Modular Forms at Supersingular Primes”, PhD thesis, University of Cambridge, 2010 
  • Lei A, “A reformulation of Kato’s main conjecture for modular forms”, Oberwolfach Reports, 8(2), 2011, 1754-1756
  • Lei A, “Local Class Field Theory”, essay for the Part III Mathematical Tripos at University of Cambridge, 2007 
  • Lei A, “Efficient Parametrisation of Rational Normal Curves”, report on a summer research project, 2006 
  • Lei A, “What so perfect about perfect numbers?”, Eureka, 58  
  • Lei A, “Brauer groups”, entry for the Yeats Essay Prize at Trinity College Cambridge, 2005