Linear dependence of quasi-periods over the rationals

Abstract

In this note we shall show that a lattice Zω1 +Zω2 in C has Q-linearly dependent quasi-periods if and only if ω2/ω1 is equivalent to a zero of the Eisenstein series E2 under the action of SL2(Z) on the upper half plane of C. 2020 Mathematics Subject Classification. 11J72, 11J89. Manuscript received 23rd March 2020, revised 7th August 2020, accepted 17th December 2020.