A truncated second main theorem for algebraic tori with moving targets and applications

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We establish a second main theorem for algebraic tori with slow growth moving targets with truncation to level 1. As the first application of this result, we prove the Green–Griffiths–Lang conjecture for projective spaces with n + 1 $n+1$ components in the context of moving targets of slow growth. Then we discuss the integrability of the ring of exponential polynomials in the ring of entire functions as another application.