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We study asymptotic relations connecting unipotent averages of $Sp(2g,\mathbb{Z})$ automorphic forms to their integrals over the moduli space of principally polarized abelian varieties.
R. Rankin, Contributions to the theory of Ramanujan’s function τ ( n ) \tau(n) and symilar arithmetical functions, Proc. Cambridge Philos. Soc. 35
1939
Earlier work this paper cites.
A. Selberg, Bemerkungen ùber eine Dirichletsche reihe, die mit der theorie der modulformen nahe verbunden ist, Arch. Math. Naturvid. 43
1940
Earlier work this paper cites.
C. L. Siegel, Symplectic geometry, Amer. J. Math. 65 (1943), 1-86; Academic Press, New York and London (1964); Gesammelte Abhandlungen, no. 41, vol. II, Springer-Verlag (1966), 274-359. C. L. Siegel, Zur Bestimmung des Volumens des Fundamental Bereichs der unimodularen Gruppe, Math. Ann. 137 (1959), 427-432
1959
Earlier work this paper cites.
H. Furstenberg, The Unique Ergodicity of the Horocycle Flow, Recent Advances in Topological Dynamics, A. Beck (ed.), Springer Verlag Lecture Notes, 318 (1972), 95-115
1972
Earlier work this paper cites.
D. Zagier, Eisenstein Series and the Riemann zeta function, Automorphic Forms, Representation Theory and Arithmetic, Studies in Math. Vol. 10, T.I.F.R., Bombay, 1981, pp. 275-301
1981
Earlier work this paper cites.
Zagier, Don, The Rankin-Selberg method for authomorphic functions which are not of rapid decay in J. Fac. Sci. Tokyo 1981
1981
Earlier work this paper cites.
P. Sarnak, ”Asymptotic behavior of periodic orbits of the horocycle flow and Eisenstein series.” Comm. Pure Appl. Math. 34 (1981), no. 6, 719–739
1981
Earlier work this paper cites.
S. G. Dani and J. Smillie, Uniform distribution of horocycle orbits for Fuchsian groups. Duke Math. J. 51 (1984), 185-194
1984
Earlier work this paper cites.
T. Yamazaki, ”Rankin-Selberg method for Siegel cusp forms”, Najoya Math J. Vol. 120 (1990), 35-49
1990
Earlier work this paper cites.
M. Ratner, Distribution rigidity for unipotent actions on homogeneous spaces. Bull. Amer. Math. Soc. (N.S.) Volume 24, Number 2 (1991), 321-325
1991
Earlier work this paper cites.
M. Ratner, Raghunathan’s topological conjecture and distributions of unipotent flows. Duke Math. J. Volume 63, Number 1 (1991), 235-280
1991
Cited alongside, same era.
D. Kutasov and N. Seiberg, “Number Of Degrees Of Freedom, Density Of States And Tachyons In String Theory And Cft,” Nucl. Phys. B 358
1991
Cited alongside, same era.
A. Verjovsky, ”Arithmetic geometry and dynamics in the unit tangent bundle of the modular orbifold”, in: Dynamical Systems (Santiago 1990), Pitman Res. Notes Math. No. 285 , Longman Sci. Tech., Harlow, 1993, pp. 263-298
1993
Cited alongside, same era.
K. Hulek, C. Kahn and S. Weintraub, “Moduli Spaces of Abelian Surfaces: Compactification, Degenerations, and Theta Functions”, De Gruyter Expositions in Mathematics 12, 1993
1993
Cited alongside, same era.
E. D’Hoker, D.H. Phong, “Two-Loop Superstrings I, Main Formulas”, Phys. Lett. B 529
S. L. Cacciatori and F. Dalla Piazza, “Two loop superstring amplitudes and S 6 S_{6} representations,” Lett. Math. Phys. 83
2008
Later among the works it cites.
S. L. Cacciatori, F. Dalla Piazza and B. van Geemen, “Modular Forms and Three Loop Superstring Amplitudes,” Nucl. Phys. B 800
2008
Later among the works it cites.
S. L. Cacciatori, F. D. Piazza and B. van Geemen, “Genus four superstring measures,” Lett. Math. Phys. 85
2008
Later among the works it cites.
A. Morozov, “NSR Superstring Measures Revisited,” JHEP 0805
2008
Later among the works it cites.
G. van der Geer, Siegel modular forms and their applications in ”The 1-2-3 of Modular Forms”, Springer (2008)
2008
Later among the works it cites.
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2002
Cited alongside, same era.
E. D’Hoker, D.H. Phong, “Two Loop Superstrings II. The Chiral measure on Moduli Space”, Nucl. Phys. B636
2002
Cited alongside, same era.
E. D’Hoker, D.H. Phong, “Two Loop Superstrings III. Slice Independence and Absence of Ambiguities”, Nucl. Phys. B636
2002
Cited alongside, same era.
E. D’Hoker, D.H. Phong, “Two-Loop Superstrings IV: The Cosmological Constant and Modular Forms”, Nucl. Phys. B 639
2002
Cited alongside, same era.
E. D’Hoker, D.H. Phong, “Asyzygies, Modular Forms, and the Superstring Measure I”, Nucl. Phys. B 710
2005
Cited alongside, same era.
E. D’Hoker, D.H. Phong, “Asyzygies, Modular Forms, and the Superstring Measure II”, Nucl. Phys. B 710
2005
Cited alongside, same era.
C. Angelantonj, M. Cardella, S. Elitzur, E. Rabinovici “ On the dependence of the effective number of closed strings degrees of freedom on the Riemann zeros “ To Appear
Cited in the paper.
2009
Later among the works it cites.
F. D. Piazza and B. van Geemen, “Siegel modular forms and finite symplectic groups,” Adv. Theor. Math. Phys. 13 (2009) 1771-1814
2009
Later among the works it cites.
S. Grushevsky, “Superstring scattering amplitudes in higher genus,” Commun. Math. Phys. 287
2009
Later among the works it cites.
A. Andrianov, ” Introduction to Siegel Modular forms and Dirichlet Series”, Springer (2009)
2009
Later among the works it cites.