1. Ahlfors L., Sario L., Riemann surfaces, Princeton University Press, Princeton, NJ 1960. MR 0114911 (22:5729) 

2. Aurell E., Salomonson P., On functional determinants of Laplacians in polygons and simplicial complexes, Commun. Math. Phys. 165, 233-259 (1994). MR 1301847 (95i:58186) 

3. Burghelea D., Friedlander L., Kappeler T., Meyer-Vietoris type formula for determinants of elliptic differential operators, J. Funct. Anal., 107 (1992), N1, 34-65. MR 1165865 (93f:58242) 

4. Cheeger, J., Spectral Geometry of singular Riemannian spaces, J. Differential Geom., 18 (1983), 575-657. MR 730920 (85d:58083) 

5. Edward J., Wu S., Determinant of the Neumann operator on smooth Jordan curves, Proceedings of the American Mathematical Society, Vol. 111, N2, 1991. MR 1031662 (91f:58094) 

6. Eskin A., Masur H., Zorich A., Moduli spaces of Abelian differentials: the principal boundary, counting problems and the Siegel-Veech constants, math.DS/0202134. 

7. Fay, John D., Theta-functions on Riemann surfaces, Lect. Notes in Math., 352, Springer (1973). MR 0335789 (49:569) 

8.Fay, John D., Kernel functions, analytic torsion, and moduli spaces, Memoirs of the AMS 464 (1992). MR 1146600 (93e:58192) 

9. Hillairet L., Contribution d'orbites périodiques diffractives à la formule de trace, Ph.D. Thesis, L'Institut Fourier, Grenoble, 2002. 

10. J. Jorgenson, Asymptotic behavior of Faltings's delta function. Duke Math. J., 61 (1990), N1, 221-254. MR 1068387 (91m:14042) 

11.Kokotov A., Korotkin D., Tau-functions on spaces of Abelian differentials and higher genus generalizations of Ray-Singer formula, Journal of Differential Geometry, 82 (2009), 35-100. MR 2504770 (2010c:58041) 

12.Kokotov A., Korotkin D., Tau-functions on the spaces of Abelian and quadratic differentials and determinants of Laplacians in Strebel metrics of finite volume, preprint of Max-Planck Institute for Mathematics in the Sciences, Leipzig, 46/2004; math.SP/0405042. 

13.Kontsevich, M., Zorich, A., Connected components of the moduli spaces of holomorphic differentials with prescribed singularities, Invent. Math. 153 631-678 (2003). MR 2000471 (2005b:32030) 

14. Yoonweon Lee, Burghelea-Friedlander-Kappeler's gluing formula for the zeta-determinant and its applications to the adiabatic decompositions of the zeta-determinant and analytic torsion, Transactions of the American Mathematical Society, Vol. 355, N10, pp. 4093-4110. MR 1990576 (2004e:58058) 

15. Loya P., McDonald P., Park J., Zeta regularized determinants for conic manifolds, Journal of Functional Analysis (2007), 242, N1, 195-229. MR 2274020 (2007g:58036) 

16. R. Lundelius, Asymptotics of the determinant of the Laplacian on hyperbolic surfaces of finite volume, Duke Math. J. 71 (1993), no. 1, 211-242. MR 1230291 (94j:58178) 

17. Masur H., The extension of the Weil-Peterson metric to the boundary of Teichmuller space, Duke Mathematical Journal, Vol. 43(1976), N3, pp. 623-635. MR 0417456 (54:5506) 

18.Ozawa S., The first eigenvalue of the Laplacian on two-dimensional Riemannian manifolds, Tohoku Math. Journ., 34(1982), 7-14. MR 651702 (83g:58073) 

19.Polchinski J., Evaluation of the one loop string path integral, Commun. Math. Phys., 104 (1986) 37-47. MR 834480 (87j:81223) 

20. Ray D. B., Singer I. M., Analytic torsion for complex manifolds. Ann. of Math. (2) 98 154-177 (1973), MR 383463, Zbl 0267.32014. 

21. Weisberger W., Conformal Invariants for determinants of Laplacians on Riemann surfaces, Commun. Math. Phys., 112, 633-638 (1987). MR 910583 (89c:58135) 

22. Wentworth R., Precise constants in bosonization formulas on Riemann surfaces, Commun. Math. Phys. 282 (2) (2008), 339-355. MR 2421480 (2009f:58054) 

23. Wentworth R., private communication. 

24. Wentworth R., Asymptotics of determinants from functional integration, J. Math. Phys., 32(7), 1991, 1767-1773. MR 1112704 (92k:58271) 

25. Wentworth R., The asymptotics of the Arakelov-Green's function and Faltings' delta invariant, Commun. Math. Phys. 137, (1991), 427-459. MR 1105425 (92g:14019) 

26.Wolpert S., Asymptotics of the spectrum and the Selberg zeta function on the space of Riemann surfaces, Comm. Math. Phys. 112 (1987), no. 2, 283-315. MR 905169 (89c:58136) 

27. Yamada A., Precise variational formulas for abelian differentials, Kodai Math. J., 3 (1980), 114-143. MR 569537 (81i:30078)