  We derive improved and easily computable upper bounds on the capacity of the
discrete-time Poisson channel under an average-power constraint and an
arbitrary constant dark current term. This is accomplished by combining a
general convex duality framework with a modified version of the digamma
distribution considered in previous work of the authors (Cheraghchi, J. ACM
2019; Cheraghchi, Ribeiro, IEEE Trans. Inf. Theory 2019). For most choices of
parameters, our upper bounds improve upon previous results even when an
additional peak-power constraint is imposed on the input.
