# List of Publications

1. Intersection Triangles of Steiner Systems, Math. Z. 139 (1974), 87-104. 2. Arithmetic on Elliptic Curves with Complex Multiplication, Thesis, Harvard University, Springer Lecture Notes 776 (1980), 96 pages. 3. (with D. Rohrlich), Some Results on the Mordell-Weil Group of the Jacobian of the Fermat Curve, Inv. Math. 44 (1978), 201-224. 4. On the Periods of Abelian Integrals and a Formula of Chowla and Selberg, Inv. Math. 45 (1978), 193-211. 5. Ramification in p-adic Lie Extensions, Asterisque 65 (1979), 81-102. 6. (with N. Koblitz), Gauss Sums and the p-adic .-function, Annals of Mathematics 109 (1979), 569-581. 7. On an identity of Chowla and Selberg. Journal of Number Theory 11 (1979), 344-348. 8. (with D. Zagier), On the critical values of Hecke L-series, Société Mathématique de France, 2e serie, Mem. No 2 (1980), 49-54. 9. (with J. Harris), Real algebraic curves, Annales Sci. de l'ÉNS 4e série, t. 14 (1981),157-182. 10. On the factorization of p-adic L-series, Inv. Math. 57 (1980), 83-95. 11. (with Leslie Federer), Regulators and Iwasawa modules, Inv. Math. 62 (1981), 443-457. 12. p-adic L-series at s = 0, J. Fac. Sci. Univ. of Tokyo 28 (1982), 979-994. 13. Minimal models for elliptic curves with complex multiplication, Compositio Mathematica 45 (1982), 155-164. 14. The Annihilation of divisor classes in abelian extensions of the rational function field, Sém. théorie des Nombres, Bordeaux, 1980-81. 15. Algebraic Hecke characters for function fields, Sem. DPP, Birkhauser, 1980-81. 16. On the conjecture of Birch and Swinnerton-Dyer for elliptic curves with complex multiplication, Proc. of a Conf. on Fermat's Last Theorem, Birkhauser, 1982. 17. Heegner points on X0(11), Sém. théorie des Nombres de Bordeaux, Exposé 34, 1982. 18. Heegner points on X0(N). In Rankin, R.A. (ed): Modular forms. Chicester: Ellis Horwood 1984, pp. 87-106. 19. (with D. Zagier), Points de Heegner et derivees de fonctions L, C. Rendus 297 (1983), 85-87. 20. (with J. Buhler and D. Zagier), On the conjecture of Birch and Swinnerton-Dyer for an Elliptic Curve of Rank 3. Math. of Computation 44 (1985), 473-481. 21. (with D. Zagier) Singular moduli. J. Crelle 355 (1985), 191-220. 22. (with J. Buhler), Arithmetic on elliptic curves with complex multiplication II. Inv. Math. 79 (1985), 11-29. 23. (with J. Lubin), The Eisenstein descent on J0(N), Inv. Math. 83 (1986), 303-319. 24. (with D. Zagier) Heegner points and derivatives of L-series. Inv. Math. 84 (1986), 225-320. 25. On canonical and quasi-canonical liftings. Inv. Math. 84 (1986), 321-326. 26. Local heights on curves. In Cornell, Silverman (ed.): Arithmetic Geometry. Springer 1986, 327-339. 27. Heights and special values of L-series. CMS Proceedings, Vol. 7, AMS (1986), 115-187. 28. Heights and L-series. Proceedings of ICM Berkeley (1986), 445-433. 29. Representation theory and the cuspidal group of X(p), Duke Math. J. 54 (1987), 67-75. 30. Heegner points and the modular curve of prime level, J. Math. Soc. Japan 39 (1987), 345362. 31. (with W. Kohnen and D. Zagier) Heegner points and derivatives of L-series II, Math. Annalen 278 (1987), 497-562. 32. (with M. Rosen) Fourier analysis and the special values of L-functions. Advances in Math. 69 (1988), 1-31. 33. On the values of abelian L-functions at s = 0, J. Fac. Science of University of Tokyo, 35 (1988), 177-197. 34. Local orders, root numbers, and modular curves, Amer. J. of Math. 110 (1988), 1153-1182. 35. (with R. Coleman) p-adic heights on curves, Adv. Studies in Pure Math. 17 (1989), 73-81. 36. A tameness criterion for Galois representations associated to modular forms (mod p), Duke Math. J., 61, (1990), 445-517. 37. Group representations and lattices, J.A.M.S., 3, (1990), 929-960. 38. Elliptic curves and modular forms, Proc. AMS Centennial (1991). 39. Kolyvagin's work on modular elliptic curves, in: L-functions and arithmetic, LMS Lecture Notes 153 (1991), 235-256. 40. Some applications of Gelfand pairs to number theory, Bull. AMS, 24, (1991), 277-301. 41. (with D. Prasad) Test vectors for linear forms, Math. Ann. 291, (1991), 343-355. 42. (with S. Kudla) On the central critical value of triple product L-functions, Compositio Math. 81, (1992), 143-209. 43. (with D. Prasad) The restriction of a representation of SO(n) to SO(n-1), Canadian Math. J., 44, (1992), 974-1002. 44. (with K. Keating) On the intersection of modular correspondences, Inv. Math. 112, (1993), 225-245. 45. L-functions at the central critical point, Proc. Symp. Pure Math., AMS, 55, (1994), Part 1, 527-535. 46. (with M. Hopkins) Equivariant vector bundles on the Lubin-Tate moduli space, Contemp. Math., AMS, 158, (1994), 23-88. 47. (with M. Hopkins) The rigid analytic period mapping, Lubin-Tate space, and stable homotopy theory, BAMS, 30, (1994), 76-86. 48. (with D. Prasad) On irreducible representations of SO2n+1xSO2m, Canadian Math. J. 46, (5) (1994), 930-950. 49. A remark on tube domains, Math. Research Letters, 1, (1994), 1-9. 50. (with N. Wallach) A distinguished family of unitary representations for the exceptional groups of real rank = 4, Lie theory and geometry, Birkhäuser, (1994), 289-304. 51. (with C. Schoen) The modified diagonal cycle on the triple product of a pointed curve, Annales Fourier, (1995), 649-679. 52. Groups over Z, Inv. Math., 124, (1996), 263-279. 53. (with N. Elkies) The exceptional cone and the Leech lattice, IMRN Research Notes 14 (1996), 665-698. 54. (with N. Wallach) On quaternionic discrete series representations, and their continuations, J. Crelle (1996), 73-123. 55. (with N. Elkies) Embeddings into integral octonions, Pacific J. Math., (1997), 147-158. 56. On the motive of G and the principal homomorphism SL2 . G, Asian J. Math. 1, (1997), 208-213. 57. On the motive of a reductive group, Inv. Math., 130 (1997), 287-313. 58. (with G. Savin) The dual pair PGL3 xG2, Canad. Math. Bull. Can. 40 (1997), 376-384. 59. On the Satake isomorphism, in: Galois representations in arithmetic algebraic geometry. LMS Lecture Notes, 254, (1998), 223-238. 60. (with G. Savin) Motives with Galois group of type G2: an exceptional theta correspondence, Compositio Math 114 (1998), 153-217. 61. Modular forms (mod p) and Galois representations, IMRN 16 (1998) 865-875, 62. (with B. Kostant, P. Raymond, and S. Sternberg) The Weyl character formula, the 1/2-spin representations, and equal rank subgroups, Proc. NAS 95 (1998), 8441-8442. 63. (with W.-T. Gan) Haar measure and the Artin conductor, Trans. AMS 351 (1999), 16911704. 64. Algebraic modular forms, Israel J. Math. 113 (1999), 61-93. 65. (with W.-T. Gan) Commutative subrings of certain non-associative rings, Math. Ann. 314 (1999), 265-283. 66. On simply-connected groups over Z with G(R) compact, Contemp. Math. AMS 249 (1999), 113-118. 67. (with N. Wallach) Restriction of small discrete series representations to symmetric subgroups, Proc. Symp. Pure Math. AMS 68 (2000), 255-272. 68. (with W.-T. Gan) Integral embeddings of cubic norm structures, J. Algebra, 233 (2000), 363-397. 69. On minuscule representations and the principal SL2, Electronic J. of Repr. Theory, 4 (2000) 225-244. 70. (with N. Elkies) Cubic rings and the exceptional Jordan algebra, Duke Math. J. 109 (2001), 383-409. 71. (with J. Harris) On some geometric constructions related to theta characteristics, In: Contributions to Automorphic Forms, Geometry, and Number Theory, Johns Hopkins Press (2004), 279-311. 72. (with W.-T. Gan and G.Savin) Fourier coefficients of modular forms on G2, Duke Math. J. 115 (2002), 105-169. 73. (with C. McMullen) Automorphisms of even unimodular lattices and unramified Salem numbers, J. of Algebra 257 (2002) 265-290. 74. Unramified reciprocal polynomials and Coxeter decompositions, Moscow Math. J. 2 (2002), 681-692. 75. (with P. Deligne) The exceptional series and its descendants, C. Rendus 335 (2002) 877-881. 76. Some remarks on signs in functional equations, Ramanujan J. 7 (2003), 91-93. 77. Heegner points and representation theory, In: Rankin L-series, MSRI Publications 49 (2004) 37-65. 78. (with G. Nebe) Globally maximal arithmetic groups, J. Algebra 272 (2004), 625-642. 79. An elliptic curve test for Mersenne primes, J. Number Theory 110(2005) 114-119. 80. (with D. Pollack) On the Euler characteristic of the discrete spectrum. J. Number Theory 110 (2005) 136-163. 81. On the centralizer of a regular, semi-simple, stable class. Electronic J. of Representation Theory 9 (2005) 287-296. 82. On the values of Artin L-functions. Quarterly Journal of Pure and Applied Mathematics 1 (2005) 1-13. 83. (with M. Reeder) From Laplace to Langlands via representations of orthogonal groups. Bulletin AMS, 43 (2006), 163-205. 84. (with J. Parson) On the local divisibility of Heegner points. In: Number Theory, analysis and geometry in memory of Serge Lang. Springer (2011) 215-242. 85. The arithmetic of elliptic curves . an update. Arabian Journal of Science and Engineering 1 (2009), 95-103. 86. (with M. Lucianovic) On cubic rings and quaternion rings. J. Number Theory 129 (2009), 1468-1478. 87. (with N. Wallach) On the Hilbert polynomials and Hilbert series of homogeneous projective varieties.In: Arithmetic geometry and automorphic forms. ALM 19. International Press (2011), 253-264. 88. (with M. Reeder) Arithmetic invariants of discrete Langlands parameters. Duke Math J. 154 (2010) 431-508. 89. (with E. Frenkel) A rigid irregular connection on the projective line. Annals of Math. 170 (2009) 1469-1512. 90. Irreducible cuspidal representations with prescribed local behavior. Amer. J. Math. 133 (2011) 1231-1258. 91. (with E. Hironaka and C. McMullen) Cyclotomic factors of Coxeter polynomials. J. Number Theory 129 (2009) 1034-1043. 92. (with W-T.Gan and D. Prasad) Symplectic root numbers, central critical values, and restriction problems in the representation theory of classical groups. In: Sur les conjectures de Gross et Prasad, Asterisque 346 (2012). 93. Rigid local systems on G_{m}with finite monodromy. Advances in Math. 224 (2010) 2531-2543.` 94. (with W-T. Gan and D.Prasad) Restriction of representations of classical groups : Examples. In: Sur les conjectures de Gross et Prasad, Asterisque 346 (2012). 95. On Bhargava's representations and Vinberg's invariant theory.In: Frontiers of mathematical sciences. International Press (2011), 317-321. 96. (with M. Bhargava) Arithmetic invariant theory. Wallach volume (2014). 97. Trivial L-functions for the rational function field. J. Number Theory 133 (2013), 970-976. 98. The classes of singular moduli in the generalized Jacobian. In: Geometry and arithmetic, Congress reports of the EMS (2012), 137-142. 99. (with M. Reeder, J-K. Yu, and P. Levy) Gradings of positive rank on simple Lie algebras. Transformation groups 17 (2012), 1123-1190. 100. Lectures on the conjecture of Birch and Swinnerton-Dyer. In: Arithmetic of L-functions, AMS PCMI publications (2011), 169-210. 101. Hanoi lectures on hyperelliptic curves. Acta mathematica vietnamica 37 (2012), 579 - 588. 102. (with M. Bhargava) The average size of the 2-Selmer group of the Jacobians of hyperelliptic curves with a rational Weierstrass point. In: Automorphic Representations and L-functions, TIFR Studies in Math 22 (2013), 23--91. 103. (with M. Bhargava and X. Wang) Arithmetic invariant theory II. Vogan volume (2015).