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Number Theory

Number Theory Research Group Publications

For publications please check individual academic staff profiles listed here.


  • D. Burns, K. Buzzard, J. Nekovar (Editors), L-Functions and Galois Representations, London Math. Soc. Lecture Note Series 320, Cambridge University Press (2007).
  • C. J. Bushnell, G. Henniart, The Local Langlands Conjecture for GL(2), Grundlehren der Mathematischen Wissenschaften 335, Springer-Verlag (2006).
  • F. Diamond, J. Shurman, A First Course in Modular Forms, Graduate Texts in Mathematics 228, Springer-Verlag (2005).
  • D. Burns, C. Popescu, J. Sands, D. Solomon (Editors), Stark's Conjectures: Recent Work and New Directions, Contemporary Mathematics 358, American Mathematical Society (2004).

Preprints (follow link)



  • C. Bushnell, G. Henniart, Langlands parameters for epipelagic representations of GLn , Math. Ann. 358 (2014), 433-463.


  • M. Kakde, The main conjecture of Iwasawa theory for totally real fields,Invent. Math. 193(2013), 539–626.
  • T. Gee, P. Kassaei, Companion forms in parallel weight one,Compositio Math. 149 (2013), 903-913.
  • M. Krishnapur, P. Kurlburg, I. Wigman, Nodal length fluctuations for arithmetic random waves, Annals of Math. 177 (2013), 699-737.
  • C. Bushnell, G. Henniart, Intertwining of simple characters in GL(n), Int. Math. Res. Notices 2013, 3977-3987.
  • J. Barrett, D. Burns, Annihilating Selmer modules, J. Reine Angew. Math. (Crelle) 675 (2013), 191-222.
  • P. Kassaei, Modularity lifting theorems in parallel weight one, J. Amer. Math. Soc.  26 (2013), 199-225.
  • C. Bushnell, G. Henniart, Modular local Langlands correspondence for GLn , Int. Math. Res. Notices (2013), doi: 10.1093/imrn/rnt063.
  • D. Burns, D. Macias Castillo, Organising matrices for arithmetic complexes, Int. Math. Res. Notices (2013), doi: 10.1093/imrn/rnt011.


  • D. Burns, R. de Jeu and H. Gangl, On special elements in higher algebraic K-theory and the Lichtenbaum-Gross Conjecture, Adv. Math. 230 (2012), 1502-1529.
  • D. Burns, On Artin formalism for the conjecture of Bloch and Kato, Math. Res. Lett. 19 (2012), 1155-1169.
  • E. Goren and P. Kassaei, Canonical Subgroups Over Hilbert Modular Varieties, J. Reine Angew. Math. (Crelle) 670 (2012), 1-63.
  • M. Kakde, From the classical to the noncommutative Iwasawa theory (for totally real number fields), in Non-abelian Fundamental Groups and Iwasawa Theory, LMS Lecture Notes 393Cambridge Univ. Press (2012) 107-131.


  • M. Breuning, Determinant functors on triangulated categories, J. K-Theory 8 (2011), 251-291.
  • D. Burns, Congruences between derivatives of geometric L-functions, with an appendix by D. Burns, K. F. Lai and K-S. Tan, Invent. Math. 184 (2011), 221-256.
  • D. Burns, On derivatives of Artin L-series, Invent. Math. 186 (2011), 291-371.
  • D. Burns and O. Venjakob, On descent theory and main conjectures in non-commutative Iwasawa theory, J. Inst. Math. Jussieu 10 (2011), 59-118.
  • D. Burns and H. Johnston, A non-abelian Stickelberger theorem, Compositio Math. 147 (2011), 35-55.
  • C. Bushnell, G. Henniart and P.C. Kutzko, Types and explicit Plancherel formulae for reductive p-adic groups, Clay Math. Institute Proceedings 13, Amer. Math. Soc. (2011), 55-80.
  • C. Bushnell and G. Henniart, The essentially tame local Jacquet-Langlands correspondence, Pure App. Math. Q. 7 (2011), 469-538.
  • C. Bushnell and G. Henniart, Explicit functorial correspondences for level zero representations of p-adic linear groups, J. Number Theory 131 (2011), 309-331.
  • C. J. Bushnell and G. Henniart, Self-dual representations of some dyadic groups, Math. Ann. 351 (2011), 67-80.
  • S. Chang and F. Diamond, Extensions of rank one (φ,Γ)-modules and crystalline representations, Compositio Math. 147 (2011), 375-427.
  • M. Kakde, Proof of the main conjecture of noncommutative Iwasawa theory for totally real number fields in certain cases, J. Alg. Geom. 20 (2011), 631-683.


  • M. Breuning and D. Burns, On equivariant Dedekind zeta-functions at s=1, Documenta Mathematica, Extra Volume Suslin (2010), 119-146.
  • D. Burns, Leading terms and values of equivariant motivic L-functions, Pure App. Math. Q. 6 (2010), 83-172 (John Tate Special Issue, Part II).
  • S. Sasaki, Analytic continuation of overconvergent Hilbert eigenforms in the totally split case, Compositio Math. 146 (2010), 541-560.
  • K. Buzzard, F. Diamond and F. Jarvis, On Serre's conjecture for mod l Galois representations over totally real fields, Duke Math. J. 155 (2010), 105-161.
  • D. Solomon, Equivariant L-Functions at s=0 and s=1 in Publications Mathematiques de Besancon, Algebre et Theorie des Nombres (2010), 129-156.
  • D. Solomon, Abelian L-Functions at s=1 and Explicit Reciprocity for Rubin-Stark Elements, Acta Arith. 143 No. 2 (2010), 145-189.
  • X.-F. Roblot and D. Solomon, Testing the Congruence Conjecture for Rubin-Stark Elements, J. Number Theory 130 (2010), 1374-1398.
  • C. Bushnell, G. Henniart and B. Lemaire, Caractère et degré formel pour les formes intérieures de GL(n) sur un corps local de caractéristique non nulle, Manuscripta Math. 131 (2010), 11-24.
  • C. Bushnell and G. Henniart, The essentially tame local Langlands correspondence, III: the general case, Proc. London Math. Soc. (3) 101 (2010), 497-553.


  • D. Burns, Algebraic p-adic L-functions in non-commutative Iwasawa theory, Publ. RIMS Kyoto 45 (2009), 75-88 (Proceedings of special semester on Arithmetic Geometry, Fall, 2006).
  • P. Kassaei, Overconvergence and classicality: the case of curves, J. Reine Angew Math. (Crelle) 631 (2009), 109--139.
  • E. Goren and P. Kassaei, Canonical Subgroups Over Hilbert Modular Varieties, C. R. Acad. Sci. Paris, Ser. I 347 (2009) 985-990.


  • D. Burns, Perfecting the nearly perfect, Pure and Applied Math. Quarterly 4 (2008), Jean-Pierre Serre Special Issue Part I, 1041-1058.
  • D. Burns, On refined Stark conjectures in the non-abelian case, Math. Research Letters 15 (2008), 841-856.
  • W. Bley and M. Breuning, Exact algorithms for p-adic fields and epsilon constant conjectures, Illinois Journal of Mathematics 52, No. 3 (2008), 773-797.
  • D. Solomon, On Twisted Zeta-Functions at s=0 and Partial Zeta-Functions at s=1, Journal of Number Theory 128 (2008), 105-143.


  • M. Breuning and D. Burns, Leading terms of Artin L-functions at s=0 and s=1, Compositio Mathematica 143 (2007), 1427-1464.
  • C. J. Bushnell and G. Henniart, Counting the discrete series for GL(n), Bull. London Math. Soc. 39  (2007), 133-137.
  • F. Diamond, A correspondence between representations of local Galois groups and Lie-type groups, in L-functions and Galois representations, (eds. D. Burns, K. Buzzard, J. Nekovar), Cambridge Univ. Press. (2007), 187-206.
  • D. Burns and A. Hayward, Explicit Units and the Equivariant Tamagawa Number Conjecture, II, Comm. Math. Helv. 82 (2007), 477-497.
  • D. Burns, Congruences between derivatives of abelian L-functions at s=0, Inventiones Math. 169 (2007), 451-499.
  • D. Burns and S. Seo, On the Galois cohomology of ideal class groups, Arch. Math. 89 (2007), 536-540.
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