REAL

MODULAR COCYCLES AND LINKING NUMBERS

Duke, W. and Imamoḡlu, Ö. and Tóth, Á. (2017) MODULAR COCYCLES AND LINKING NUMBERS. DUKE MATHEMATICAL JOURNAL, 166 (6). pp. 1179-1210. ISSN 0012-7094

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Abstract

It is known that the 3-manifold SL(2, Z) \ SL(2, R) is diffeomorphic to the complement of the trefoil knot in S-3. E. Ghys showed that the linking number of this trefoil knot with a modular knot is given by the Rademacher symbol, which is a homogenization of the classical Dedekind symbol. The Dedekind symbol arose historically in the transformation formula of the logarithm of Dedekind's eta function under SL(2, Z). In this paper we give a generalization of the Dedekind symbol associated to a fixed modular knot. This symbol also arises in the transformation formula of a certain modular function. It can be computed in terms of a special value of a certain Dirichlet series and satisfies a reciprocity law. The homogenization of this symbol, which generalizes the Rademacher symbol, gives the linking number between two distinct symmetric links formed from modular knots.

Item Type: Article
Uncontrolled Keywords: FORMS; Cycle integrals; RATIONAL PERIOD FUNCTIONS
Subjects: Q Science / természettudomány > QA Mathematics / matematika
SWORD Depositor: MTMT SWORD
Depositing User: MTMT SWORD
Date Deposited: 15 May 2018 13:56
Last Modified: 15 May 2018 13:56
URI: http://real.mtak.hu/id/eprint/79724

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