Theta functions

By W. Reinhardt, P. Walker. NIST Handbook of Mathematical Functions, 2010

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The Picard group of the moduli space of curves with level structures (2009, background): “It is known that H g /Sp2g(Z,L) is a quasiprojective variety for all L (see [29] for a proof and history of this result).”
Open string amplitudes and large order behavior in topological string theory (2006, methodology): “The appearance of the determinant of the inner products of the χi is typical for computations which use the Quillen anomaly (see for example [10]).”
Theta height and Faltings height (2009, unknown): “, L , ϕ, ( ε P ) P ∈ A r 2 ) rational over K . tome 140 – 2012 – n o 1”
On Algebraic Expressions of Sigma Functions for (n,s) Curves (2008, background): “Integrating this formula we get Proposition 1 [16, 17] For ã, b̃, c̃, d̃ ∈ X̃,”
Torus bundles not distinguished by TQFT invariants (2011, background): “The theta functions construction was generalized in Funar [28] to quantizations of multidimensional tori endowed with Coxeter group actions.”
The Schottky Problem (2010, background): “4 (Igusa [Igu72] for ` = 4n2; Mumford for ` ≥ 3, Salvati Manni [SM94] for `≥ 2).”