Abstract
To find whether on a toroidal group ¢n/Γ any meromorphic function can be written as the quotient of two θ-functions associated with the lattice Γ one has to study the existence of ℤn-periodic entire solutions of a system of difference equations. The formal series solutions are shown to converge "generically". This gives a partial answer to a question of A. Andreotti as to find "good conditions" for the convergence of the series that occur in the construction of the θ-functions associated with Γ.
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References
CONFORTO, F., Abelsche Funktionen und algebraische Geometrie, Springer-Verlag, Berlin 1956.
SCHMIDT, W.M., Approximation to algebraic numbers, L'Enseignement Mathématique XVII (3–4) (1971), 187–253.
VOGT, C., Geradenbündel auf toroiden Gruppen, Dissertation, Dusseldorf 1981.
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© 1985 Springer-Verlag
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Weill, G.G. (1985). A remark on the convergence of series occuring in the construction of θ-functions on a toroidal group. In: Ławrynowicz, J. (eds) Seminar on Deformations. Lecture Notes in Mathematics, vol 1165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076167
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DOI: https://doi.org/10.1007/BFb0076167
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