TY - JOUR

T1 - Generalised Kummer constructions and Weil restrictions

AU - Cynk, Sławomir

AU - Schütt, Matthias

N1 - Funding information: This paper originated from discussions while the first author visited Universität Hannover. Support by the DFG Schwerpunkt 1094 “Globale Methoden in der komplexen Geometrie” is gratefully acknowledged. We particularly thank K. Hulek. The paper was finished while the second author enjoyed the hospitality of Harvard University, sponsored by DFG-grants Schu 2266/2-1 and Schu 2266/2-2. We are also grateful to the referee for helpful suggestions.

PY - 2009/8

Y1 - 2009/8

N2 - We use a generalised Kummer construction to realise all but one known weight four newforms with complex multiplication and rational Fourier coefficients in Calabi-Yau threefolds defined over Q. The Calabi-Yau manifolds are smooth models of quotients of the Weil restrictions of elliptic curves with CM of class number three.

AB - We use a generalised Kummer construction to realise all but one known weight four newforms with complex multiplication and rational Fourier coefficients in Calabi-Yau threefolds defined over Q. The Calabi-Yau manifolds are smooth models of quotients of the Weil restrictions of elliptic curves with CM of class number three.

KW - Calabi-Yau threefold

KW - Complex multiplication

KW - Modular form

KW - Weil restriction

UR - http://www.scopus.com/inward/record.url?scp=67349113865&partnerID=8YFLogxK

UR - https://arxiv.org/abs/0710.4565

U2 - 10.1016/j.jnt.2008.09.010

DO - 10.1016/j.jnt.2008.09.010

M3 - Article

AN - SCOPUS:67349113865

VL - 129

SP - 1965

EP - 1975

JO - Journal of number theory

JF - Journal of number theory

SN - 0022-314X

IS - 8

ER -