On the twoq-analogue logarithmic functions:

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Abstract
There is a simple, multi-sheet Riemann surface associated with 's inverse function for . A principal sheet for can be defined. However, the topology of the Riemann surface for changes each time q increases above the collision point of a pair of the turning points of . There is also a power series representation for . An infinite-product representation for is used to obtain the ordinary natural logarithm and the values of the sum rules for the zeros of . For , where . The values of the sum rules for the q-trigonometric functions, and , are q-deformations of the usual Bernoulli numbers.

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