String-Theory Realization of Modular Forms for Elliptic Curves with Complex Multiplication View Full Text


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Article Info

DATE

2019-04

AUTHORS

Satoshi Kondo, Taizan Watari

ABSTRACT

It is known that the L-function of an elliptic curve defined over Q is given by the Mellin transform of a modular form of weight 2. Does that modular form have anything to do with string theory? In this article, we address a question along this line for elliptic curves that have complex multiplication defined over number fields. So long as we use diagonal rational N=(2,2) superconformal field theories for the string-theory realizations of the elliptic curves, the weight-2 modular form turns out to be the Boltzmann-weighted (qL0-c/24-weighted) sum of U(1) charges with FeπiF insertion computed in the Ramond sector. More... »

PAGES

89-126

References to SciGraph publications

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  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00220-019-03302-0

    DOI

    http://dx.doi.org/10.1007/s00220-019-03302-0

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