Number Theory

Discontinuous Groups and Automorphic Forms

11Fxx

  1. Scott Ahlgren, On the irreducibility of Hecke polynomials, Math. Comp. 77 (2008), no. 263, 1725–1731.[MR]
  2. Scott Ahlgren and Ken Ono, Arithmetic of singular moduli and class polynomials, Compos. Math. 141 (2005), no. 2, 293–312.[MR]
  3. A. O. L. Atkin, Wen-Ching Winnie Li, and Ling Long, On Atkin and Swinnerton-Dyer congruence relations (II), Math. Ann. 340 (2008), no. 2, 335–358.[MR/arXiv]
  4. Tobias Berger, An Eisenstein ideal for imaginary quadratic fields and the Bloch-Kato conjecture for Hecke characters, preprint (2007), 26 pages.[arXiv]
  5. Tobias Berger and Krzysztof Klosin, A deformation problem for Galois representations over imaginary quadratic fields, J. Inst. Math. Jussieu, to appear (2009), 19.
  6. Alexander Berkovich and William C. Jagy, Ternary quadratic forms, modular equations and certain positivity conjectures, The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, Springer, New York, 2009, pp. 211–241.[doi]
  7. Siegfried Boecherer and Gabriele Nebe, On theta series attached to maximal lattices and their adjoints, preprint (2009), 16 pages.[arXiv]
  8. Johan Bosman, On the computation of Galois representations associated to level one modular forms, preprint (2007), 15 pages.[arXiv]
  9. Jim Brown, Saito-Kurokawa lifts and applications to the Bloch-Kato conjecture, Compos. Math. 143 (2007), no. 2, 290–322.[MR]
  10. Jan Hendrik Bruinier and Tonghai Yang, CM-values of Hilbert modular functions, Invent. Math. 163 (2006), no. 2, 229-288.
  11. Yann Bugeaud, Maurice Mignotte, and Samir Siksek, A multi-Frey approach to some multi-parameter families of Diophantine equations, Canad. J. Math. 60 (2008), no. 3, 491–519.[MR/link]
  12. Cecilia Busuioc, The Steinberg symbol and special values of L-functions, Trans. Amer. Math. Soc. 360 (2008), no. 11, 5999–6015.[MR]
  13. Kevin Buzzard, Questions about slopes of modular forms, Astérisque (2005), no. 298, 1–15.[MR]
  14. Kevin Buzzard and Frank Calegari, A counterexample to the Gouvêa-Mazur conjecture, C. R. Math. Acad. Sci. Paris 338 (2004), no. 10, 751–753.[MR]
  15. Kevin Buzzard and William A. Stein, A mod five approach to modularity of icosahedral Galois representations, Pacific J. Math. 203 (2002), no. 2, 265–282.[MR]
  16. Bryden Cais, Serre's conjectures, Preprint (2005), 21 pages.[link]
  17. Frank Calegari and Nathan M. Dunfield, Automorphic forms and rational homology 3-spheres, Geom. Topol. 10 (2006), 295–329 (electronic).[MR/arXiv]
  18. Frank Calegari and William A. Stein, Conjectures about discriminants of Hecke algebras of prime level, Algorithmic Number Theory, Lecture Notes in Comput. Sci., vol. 3076, Springer, Berlin, 2004, pp. 140–152.[MR]
  19. Imin Chen, Ian Kiming, and Jonas B. Rasmussen, On congruences mod pm between eigenforms and their attached Galois representations, J. Number Theory 130 (2010), no. 3, 608–619.[MR/doi]
  20. C. J. Cummins, Congruence subgroups of groups commensurable with PSL(2,Z) of genus 0 and 1, Experiment. Math. 13 (2004), no. 3, 361–382.[MR]
  21. C. J. Cummins, On conjugacy classes of congruence subgroups of PSL(2,R), LMS J. Comput. Math. 12 (2009), 264–274.[MR/doi]
  22. Henri Darmon and Robert Pollack, Efficient calculation of Stark-Heegner points via overconvergent modular symbols, Israel J. Math. 153 (2006), 319–354.[MR]
  23. Lassina Dembélé, Explicit computations of Hilbert modular forms on Q(√5), Experiment. Math. 14 (2005), no. 4, 457–466.[MR]
  24. Lassina Dembélé, Quaternionic Manin symbols, Brandt matrices, and Hilbert modular forms, Math. Comp. 76 (2007), no. 258, 1039–1057 (electronic).[MR]
  25. Lassina Dembélé, On the computation of algebraic modular forms on compact inner forms of GSp4, preprint (2009), 21 pages.[arXiv]
  26. Lassina Dembélé and Steve Donnelly, Computing Hilbert modular forms over fields with nontrivial class group, Algorithmic number theory, Lecture Notes in Comput. Sci., vol. 5011, Springer, Berlin, 2008, pp. 371–386.[MR/doi]
  27. Lassina Dembele, Matthew Greenberg, and John Voight, Nonsolvable number fields ramified only at 3 and 5, preprint (2009), 18 pages.[arXiv]
  28. Tobias Dern and Aloys Krieg, Graded rings of Hermitian modular forms of degree 2, Manuscripta Math. 110 (2003), no. 2, 251–272.[MR]
  29. Tobias Dern and Aloys Krieg, The graded ring of Hermitian modular forms of degree 2 over Q(√-2), J. Number Theory 107 (2004), no. 2, 241–265.[MR]
  30. Michael Dewar and Olav K. Richter, Ramanujan congruences for Siegel modular forms, preprint (2009), 11 pages.[arXiv]
  31. Meghan DeWitt and Darrin Doud, Finding Galois representations corresponding to certain Hecke eigenclasses, Int. J. Number Theory 5 (2009), no. 1, 1–11.[MR/doi]
  32. Luis Dieulefait, E. Gonzalez-Jimenez, and J. Jimenez Urroz, On fields of definition of torsion points of elliptic curves with complex multiplication, preprint (2009).[arXiv]
  33. Luis Dieulefait and Xavier Taixes i Ventosa, Congruences between modular forms and lowering the level mod ln, Journal de Theorie des Nombres de Bordeaux 31 (2009), no. 1, 109–118.[arXiv]
  34. Darrin Doud, Three-dimensional Galois representations with conjectural connections to arithmetic cohomology, Number Theory for the Millennium I (Urbana, IL, 2000), A K Peters, Natick, MA, 2002, pp. 365–375.[MR]
  35. Darrin Doud, Distinguishing contragredient Galois representations in characteristic two, Rocky Mountain J. Math. 38 (2008), no. 3, 835–848.[MR]
  36. Darrin Doud and Brian Hansen, Explicit Frobenius calculations supporting a generalization of a conjecture of Serre, JP J. Algebra Number Theory Appl. 6 (2006), no. 2, 381–398.[MR/link]
  37. Neil Dummigan, William Stein, and Mark Watkins, Constructing elements in Shafarevich-Tate groups of modular motives, Number Theory and Algebraic Geometry, London Math. Soc. Lecture Note Ser., vol. 303, Cambridge Univ. Press, Cambridge, 2003, pp. 91–118.[MR]
  38. Bas Edixhoven, Comparison of integral structures on spaces of modular forms of weight two, and computation of spaces of forms mod 2 of weight one, J. Inst. Math. Jussieu 5 (2006), no. 1, 1–34.[MR]
  39. Liqun Fang, J. William Hoffman, Benjamin Linowitz, Andrew Rupinski, and Helena Verrill, Modular forms on noncongruence subgroups and Atkin-Swinnerton-Dyer relations, Experiment. Math. 19 (2010), no. 1, 1–27.[arXiv]
  40. Julio Fernández, Josep González, and Joan-C. Lario, Plane quartic twists of X(5,3), Canad. Math. Bull. 50 (2007), no. 2, 196–205.[MR]
  41. Sharon M. Frechette, A classical characterization of newforms with equivalent eigenforms in Sk+1/2(4N,χ), J. London Math. Soc. (2) 68 (2003), no. 3, 563–578.[MR]
  42. E. Freitag and R. Salvati Manni, Some Siegel threefolds with a Calabi-Yau model II, preprint (2010), 23 pages.[arXiv]
  43. Eberhard Freitag and Manabu Oura, A theta relation in genus 4, Nagoya Math. J. 161 (2001), 69–83.[MR]
  44. Edray Goins, On the modularity of wildly ramified Galois representations, preprint (2004), 31 pages.[arXiv]
  45. Enrique Gonzalez-Jimenez and Xavier Guitart, On the modularity level of modular abelian varieties over number fields, J. Number Theory 130 (2010), no. 7, 1560–1570.[arXiv]
  46. Matthew Greenberg and John Voight, Computing systems of Hecke eigenvalues associated to Hilbert modular forms, Math. Comp., to appear (2011), 21 pages.[arXiv]
  47. Xavier Guitart and Jordi Quer, Modular abelian varieties over number fields, preprint (2009), 24 pages.[arXiv]
  48. P. E. Gunnells, F. Hajir, and D. Yasaki, Modular forms and elliptic curves over the field of fifth roots of unity, preprint (2010), 22 pages.[arXiv]
  49. Jerome W. Hoffman, Ling Long, and Helena Verrill, On l-adic representations for a space of noncongruence cuspforms, preprint (2010).[arXiv]
  50. Samar Jaafar and Kamal Khuri-Makdisi, On the maps from X(4p) to X(4), preprint (2007), 11 pages.[arXiv]
  51. Rafe Jones and Jeremy Rouse, Iterated endomorphisms of abelian algebraic groups, Proc. London Math. Soc. 100 (2010), 763–794.[doi/arXiv]
  52. Hidenori Katsurada, Exact standard zeta values of Siegel modular forms, Experiment. Math. 19 (2010), no. 1, 65–77.[link]
  53. L. J. P. Kilford, Slopes of overconvergent modular forms, PhD Thesis, Imperial College, University of London, 2002.[link]
  54. L. J. P. Kilford, Generating spaces of modular forms with η-quotients, JP J. Algebra Number Theory Appl. 8 (2007), no. 2, 213–226.[MR/arXiv]
  55. L. J. P. Kilford, Modular forms, Imperial College Press, London, 2008, pp. xxii+224.[MR]
  56. L. J. P. Kilford, On mod p modular representations which are defined over Fp, Glas. Mat. Ser. III 43(63) (2008), no. 1, 1–6.[MR/arXiv]
  57. L. J. P. Kilford, On the slopes of the U5 operator acting on overconvergent modular forms, J. Théor. Nombres Bordeaux 20 (2008), no. 1, 165–182.[MR/arXiv]
  58. L. J. P. Kilford, Experimental finding of modular forms for noncongruence subgroups, preprint (2009), 12 pages.[arXiv]
  59. L. J. P. Kilford, On the Up operator acting on p-adic overconvergent modular forms when X0(p) has genus 1, J. Number Theory 130 (2010), no. 3, 586–594.[MR/doi/arXiv]
  60. L. J. P. Kilford and Gabor Wiese, On the failure of the Gorenstein property for Hecke algebras of prime weight, Experiment. Math. 17 (2008), no. 1, 37–52.[MR/arXiv]
  61. L. J. P. Kilford and Gabor Wiese, On mod p representations which are defined over Fp: ii, Glasgow Math. J. 52 (2010), 391–400.[doi]
  62. Ian Kiming, Matthias Schuett, and Helena Verrill, Lifts of projective congruence groups, J. London Math. Soc, to appear (2010), 25 pages.[arXiv]
  63. Ingo Herbert Klöcker, Modular forms for the orthogonal group O(2,5), PhD Thesis, 2005.
  64. Aristides Kontogeorgis and Yifan Yang, Automorphisms of hyperelliptic modular curves X0(N) in positive characteristic, LMS J. Comput. Math. 13 (2010), 144-163.
  65. A. Krieg, The graded ring of quaternionic modular forms of degree 2, Math. Z. 251 (2005), no. 4, 929–942.[MR]
  66. Dominic Lanphier, Combinatorics of Maass-Shimura operators, J. Number Theory 128 (2008), no. 8, 2467–2487.[MR]
  67. Joan-C. Lario and René Schoof, Some computations with Hecke rings and deformation rings, Experiment. Math. 11 (2002), no. 2, 303–311.[MR]
  68. Mark Lingham, Modular Forms and Elliptic Curves over Imaginary Quartic Fields, PhD Thesis, University of Nottingham, 2005.
  69. David Loeffler, Explicit calculations of automorphic forms for definite unitary groups, LMS J. Comput. Math. 11 (2008), 326–342.[MR]
  70. David Loeffler and Jared Weinstein, On the computation of local components of a newform, preprint (2010), 21 pages.[arXiv]
  71. Ling Long, On Atkin and Swinnerton-Dyer congruence relations. III, J. Number Theory 128 (2008), no. 8, 2413–2429.[MR/arXiv]
  72. A. Marschner and J. Müller, On a certain algebra of higher modular forms, Algebra Colloq. 16 (2009), 371–380.
  73. Barry Mazur, William Stein, and John Tate, Computation of p-adic heights and log convergence, Doc. Math. (2006), no. Extra Vol., 577–614 (electronic).[MR]
  74. Marcel Mohyla and Gabor Wiese, A computational study of the asymptotic behaviour of coefficient fields of modular forms, preprint (2009), 19 pages.[arXiv]
  75. G. Nebe, Kneser-Hecke-operators in coding theory, Abh. Math. Sem. Univ. Hamburg 76 (2006), 79–90.[MR]
  76. Gabriele Nebe and Maria Teider, Hecke actions on certain strongly modular genera of lattices, Arch. Math. (Basel) 84 (2005), no. 1, 46–56.[MR]
  77. Ken Ono, The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and q-series, CBMS Regional Conference Series in Mathematics, vol. 102, Published for the Conference Board of the Mathematical Sciences, Washington, DC, 2004, pp. viii+216.[MR]
  78. Manabu Oura, Cris Poor, and David S. Yuen, Towards the Siegel ring in genus four, Int. J. Number Theory 4 (2008), no. 4, 563–586.[MR]
  79. Ariel Pacetti and Fernando Rodriguez Villegas, Computing weight 2 modular forms of level p2, Math. Comp. 74 (2005), no. 251, 1545–1557 (electronic).[MR]
  80. Kathleen L. Petersen, One-cusped congruence subgroups of Bianchi groups, Math. Ann. 338 (2007), no. 2, 249–282.[MR]
  81. Francesco Dalla Piazza and Bert van Geemen, Siegel modular forms and finite symplectic groups, preprint (2008), 33 pages.[arXiv]
  82. Robert Pollack, On the p-adic L-function of a modular form at a supersingular prime, Duke Math. J. 118 (2003), no. 3, 523–558.[MR]
  83. Alexandru A. Popa, Central values of Rankin L-series over real quadratic fields, Compos. Math. 142 (2006), no. 4, 811–866.[MR]
  84. Jordi Quer, Fields of definition of building blocks, Math. Comp. 78 (2009), no. 265, 537–554.[MR]
  85. Jeremy Rouse, Bounds for the coefficients of powers of the Delta-function, Bull. London Math. Soc. 40 (2008), no. 6, 1081-1090.[doi]
  86. Emmanuel Royer, Evaluating convolution sums of the divisor function with quasimodular forms, Int. J. Number Theory 3 (2007), no. 2, 231–261.[arXiv]
  87. Michael M. Schein, Weights in Serre's conjecture for Hilbert modular forms: the ramified case, Israel J. Math. 166 (2008), 369–391.[MR]
  88. Mehmet Haluk Şengün, The nonexistence of certain representations of the absolute Galois group of quadratic fields, Proc. Amer. Math. Soc. 137 (2009), no. 1, 27–35.[MR]
  89. William A. Stein, Explicit Approaches to Modular Abelian Varieties, PhD Thesis, University of California, Berkeley, 2000.
  90. William Stein, Modular Forms: A Computational Approach, Graduate Studies in Mathematics, vol. 79, American Mathematical Society, Providence, RI, 2007, pp. xvi+268.[MR]
  91. William A. Stein, An introduction to computing modular forms using modular symbols, Algorithmic number theory: lattices, number fields, curves and cryptography, Math. Sci. Res. Inst. Publ., vol. 44, Cambridge Univ. Press, Cambridge, 2008, pp. 641–652.[MR]
  92. William A. Stein and Helena A. Verrill, Cuspidal modular symbols are transportable, LMS J. Comput. Math. 4 (2001), 170–181 (electronic).[MR]
  93. Xavier Taixes i Ventosa and Gabor Wiese, Computing congruences of modular forms and Galois representations modulo prime powers, preprint (2009), 26 pages.[arXiv]
  94. Helena A. Verrill, Transportable modular symbols and the intersection pairing, Algorithmic Number Theory (Sydney, 2002), Lecture Notes in Comput. Sci., vol. 2369, Springer, Berlin, 2002, pp. 219–233.[MR]
  95. John Voight, Computing fundamental domains for Fuchsian groups, J. Théor. Nombres Bordeaux 21 (2009), no. 2, 469–491.[MR/link]
  96. Gabor Wiese, Dihedral Galois representations and Katz modular forms, Doc. Math. 9 (2004), 123–133 (electronic).[MR]
  97. Gabor Wiese, Modular Forms of Weight One over Finite Fields, PhD Thesis, Universiteit Leiden, 2005.
  98. Gabor Wiese, On the faithfulness of parabolic cohomology as a Hecke module over a finite field, J. reine angew. Math. 606 (2007), 79–103.[MR]
  99. Gabor Wiese, On projective linear groups over finite fields as Galois groups over the rational numbers, Edixhoven, Bas et al., Modular forms on Schiermonnikoog. Based on the conference on modular forms, Schiermonnikoog, Netherlands, October 2006, Cambridge University Press, Cambridge, 2008, pp. 343–350.[arXiv]
  100. Gabor Wiese, On modular symbols and the cohomology of Hecke triangle surfaces, Int. J. Number Theory 5 (2009), no. 1, 89–108.[MR/arXiv]
  101. Dan Yasaki, Integral cohomology of certain Picard modular surfaces, preprint (2007), 14 pages.[arXiv]
  102. Dan Yasaki, Elliptic points of the Picard modular group, Monatsh. Math. 156 (2009), no. 4, 391–396.[MR]
  103. Jahan Zahid, Zeros of p-adic forms, J. Number Theory 129 (2009), no. 10, 2439–2456.[MR/doi]
  104. David Zywina, A refinement of Koblitz's conjecture, preprint (2009).[arXiv]