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What is Theta Convolution in Elliptic Curves about?

This paper develops a modified version of the Hodge-Arakelov Comparison Isomorphism called the Theta-Convoluted Comparison Isomorphism. The key result is that the coefficients of the Fourier transform of certain algebraic theta functions are invertible away from the divisor at infinity, where elliptic curves degenerate. This allows modification of the étale side of the comparison isomorphism in a way that preserves the Galois action needed for arithmetic applications. The proof involves analyzing the degree

Author

seanbyram

Language

EN