The asymptotic distribution of traces of Maass–Poincaré series
Tài liệu tham khảo
Blomer, 2008, Hybrid bounds for twisted L-functions, J. Reine Angew. Math., 621, 53
Borcherds, 1998, Automorphic forms with singularities on Grassmannians, Invent. Math., 132, 491, 10.1007/s002220050232
Borcherds, 1998, What is Moonshine?, extra vol. I, 607
Bringmann, 2007, Arithmetic properties of coefficients of half-integral weight Maass–Poincaré series, Math. Ann., 337, 591, 10.1007/s00208-006-0048-0
Bringmann, 2007, An arithmetic formula for the partition function, Proc. Amer. Math. Soc., 135, 3507, 10.1090/S0002-9939-07-08883-1
Bringmann, 2007, Lifting cusp forms to Maass forms with an application to partitions, Proc. Natl. Acad. Sci. USA, 104, 3725, 10.1073/pnas.0611414104
Bruinier, 2002, Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors, vol. 1780
Bruinier, 2006, Hilbert class polynomials and traces of singular moduli, Math. Ann., 334, 373, 10.1007/s00208-005-0723-6
Darmon, 1994, Heegner points, Heegner cycles, and congruences, vol. 4, 45
Duke, 2006, Modular functions and the uniform distribution of CM points, Math. Ann., 334, 241, 10.1007/s00208-005-0706-7
Duke, 2007, An introduction to the Linnik problems, vol. 237, 197
Duke, 2008, Integral traces of singular values of weak Maass forms, Algebra Number Theory, 2, 573, 10.2140/ant.2008.2.573
Fay, 1977, Fourier coefficients of the resolvent for a Fuchsian group, J. Reine Angew. Math., 293–294, 143
Folsom, 2010, Equidistribution of Heegner points and the partition function, Math. Ann., 348, 289, 10.1007/s00208-010-0478-6
Gross, 1987, Heegner points and derivatives of L-series. II, Math. Ann., 278, 497, 10.1007/BF01458081
Gross, 1986, Heegner points and derivatives of L-series, Invent. Math., 84, 225, 10.1007/BF01388809
Harcos, 2006, The subconvexity problem for Rankin–Selberg L-functions and equidistribution of Heegner points. II, Invent. Math., 163, 581, 10.1007/s00222-005-0468-6
Hejhal, 1983, The Selberg Trace Formula for PSL2(R), vol. 1001
Iwaniec, 2002, Spectral Methods of Automorphic Forms, vol. 53
Iwaniec, 2004, Analytic Number Theory, vol. 53
B.D. Kim, R. Masri, T.H. Yang, Nonvanishing of Hecke L-functions and the Bloch–Kato conjecture, Math. Ann., doi:10.1007/s00208-010-0521-7, in press.
Kohnen, 1985, Fourier coefficients of modular forms of half-integral weight on Γ0(4), Math. Ann., 271, 237, 10.1007/BF01455989
Lerche, 1989, Lattices and strings, Phys. Rep., 177, 1, 10.1016/0370-1573(89)90077-X
Miller, 2010, Arithmetic traces of non-holomorphic modular invariants, Int. J. Number Theory, 6, 69, 10.1142/S1793042110002818
Niebur, 1973, A class of nonanalytic automorphic functions, Nagoya Math. J., 52, 133, 10.1017/S0027763000015932
Ono, 2007, Singular moduli generating functions for modular curves and surfaces, vol. 7, 185
K. Ono, Unearthing the visions of a master: harmonic Maass forms and number theory, Harvard-MIT Current Developments in Mathematics, International Press, 2008, preprint.
Rademacher, 1943, On the expansion of the partition function in a series, Ann. of Math., 44, 416, 10.2307/1968973
Waldspurger, 1985, Sur les valeurs de certaines fonctions L automorphes en leur centre de symétrie, Compos. Math., 54, 173
Watson, 1966
Zagier, 2002, Traces of singular moduli, vol. 3, I, 211
Zhang, 2001, Gross–Zagier formula for GL2, Asian J. Math., 5, 183, 10.4310/AJM.2001.v5.n2.a1