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Closed string amplitudes at genus $h\leq 3$ are given by integrals of Siegel modular functions on a fundamental domain of the Siegel upper half-plane.
H. M. A. Speiser and H. Weyl, “Gesammelte Abhandlungen von Hermann Minkowski
1911
Earlier work this paper cites.
C. L. Siegel, “The volume of the fundamental domain for some infinite groups.,” Trans. Am. Math. Soc
1936
Earlier work this paper cites.
C. S. Herz, “Bessel functions of matrix argument.,” Ann. Math. (2)
1955
Earlier work this paper cites.
E. Gottschling, “Explizite Bestimmung der Randflächen des Fundamentalbereiches der Modulgruppe zweiten Grades.,” Math. Ann
1959
Earlier work this paper cites.
H. Maass, “Siegel’s modular forms and Dirichlet series. Course given at the University of Maryland, 1969-1970..” Lecture Notes in Mathematics. 216. Berlin-Heidelberg-New York: Springer-Verlag. 328 p. DM 20.00; $ 5.50 (1971)., 1971
1971
Earlier work this paper cites.
A. Andrianov, “Euler products corresponding to Siegel modular forms of genus 2.,” Russ. Math. Surv
1974
Earlier work this paper cites.
V. Kalinin, “Eisenstein series on the symplectic group.,” Math. USSR, Sb
1977
Earlier work this paper cites.
D. Zagier, “The Rankin-Selberg method for automorphic functions which are not of rapid decay,” J. Fac. Sci. Univ. Tokyo Sect. IA Math
1982
Earlier work this paper cites.
G. Shimura, “On Eisenstein series.,” Duke Math. J
1983
Earlier work this paper cites.
B. McClain and B. D. B. Roth, “Modular invariance for interacting bosonic strings at finite temperature,” Commun.Math.Phys
1987
Earlier work this paper cites.
K. O’Brien and C. Tan, “Modular Invariance of Thermopartition Function and Global Phase Structure of Heterotic String,” Phys.Rev
1987
Earlier work this paper cites.
D. Gordon, D. Grenier, and A. Terras, “Hecke operators and the fundamental domain for SL(3, ℤ ) {\mathbb{Z}}) .,” Math. Comput
1987
Earlier work this paper cites.
W. Lerche, B. Nilsson, A. Schellekens, and N. Warner, “Anomaly cancelling terms from the elliptic genus,” Nucl.Phys
1988
Earlier work this paper cites.
T. Yamazaki, “Rankin-Selberg method for Siegel cusp forms.,” Nagoya Math. J
1990
Earlier work this paper cites.
L. J. Dixon, V. Kaplunovsky, and J. Louis, “Moduli dependence of string loop corrections to gauge coupling constants,” Nucl. Phys
1991
Cited alongside, same era.
D. Grenier, “On the shape of fundamental domains in GL ( n , ℝ ) / O ( n ) \text{GL}(n,{\mathbb{R}})/\text{O}(n) .,” Pac. J. Math
1993
Cited alongside, same era.
S.-i. Mizumoto, “Eisenstein series for Siegel modular groups.,” Math. Ann
1993
Cited alongside, same era.
J. A. Harvey and G. W. Moore, “On the algebras of BPS states,” Commun. Math. Phys
1998
Cited alongside, same era.
N. A. Obers and B. Pioline, “Eisenstein series and string thresholds,” Commun. Math. Phys
2000
Cited alongside, same era.
M. B. Green, H.-h. Kwon, and P. Vanhove, “Two loops in eleven dimensions,” Phys. Rev
S. Brannetti, M. Melo, and F. Viviani, “On the tropical Torelli map.,” Adv. Mat
2011
Later among the works it cites.
2012
Later among the works it cites.
C. Angelantonj, I. Florakis, and B. Pioline, “One-Loop BPS amplitudes as BPS-state sums,” JHEP
2012
Later among the works it cites.
M. Chan, “Combinatorics of the tropical Torelli map.,” Algebra Number Theory
2012
Later among the works it cites.
2013
Later among the works it cites.
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2000
Cited alongside, same era.
E. D’Hoker, M. Gutperle, and D. H. Phong, “Two-loop superstrings and S-duality,” Nucl. Phys
2005
Cited alongside, same era.
2009
Cited alongside, same era.
B. Pioline and D. Persson, “The automorphic NS5-brane,” Commun. Num. Th. Phys
2009
Cited alongside, same era.
2010
Cited alongside, same era.
2010
Cited alongside, same era.
L. Caporaso and F. Viviani, “Torelli theorem for graphs and tropical curves.,” Duke Math. J
2010
Cited alongside, same era.
H. Gomez and C. R. Mafra, “The closed-string 3-loop amplitude and S-duality,” JHEP
2013
Later among the works it cites.
E. D’Hoker and M. B. Green, “Zhang-Kawazumi invariants and superstring amplitudes.,” J. Number Theory
2014
Later among the works it cites.
B. Pioline, “Rankin-Selberg methods for closed string amplitudes,” Proc.Symp.Pure Math
2014
Later among the works it cites.
2015
Later among the works it cites.
2015
Later among the works it cites.
2015
Later among the works it cites.
B. Pioline, “ D 6 D^{6} R 4 R^{4} amplitudes in various dimensions,” JHEP
2015
Later among the works it cites.
2015
Later among the works it cites.