What is the function of epidermal ridges on human fingers (that produce fingerprints)?
I found many plausible claims that fingerprints increase friction. However, the following article claims, at least under their experimental conditions, that fingerprints actually decrease friction with smooth surfaces by reducing contact area.
Fingerprints are unlikely to increase the friction of primate fingerpads.

It is generally assumed that fingerprints improve the grip of primates, but the efficiency of their ridging will depend on the type of frictional behaviour the skin exhibits. Ridges would be effective at increasing friction for hard materials, but in a rubbery material they would reduce friction because they would reduce contact area. In this study we investigated the frictional performance of human fingertips on dry acrylic glass using a modified universal mechanical testing machine, measuring friction at a range of normal loads while also measuring the contact area. Tests were carried out on different fingers, fingers at different angles and against different widths of acrylic sheet to separate the effects of normal force and contact area. The results showed that fingertips behaved more like rubbers than hard solids; their coefficients of friction fell at higher normal forces and friction was higher when fingers were held flatter against wider sheets and hence when contact area was greater. The shear stress was greater at higher pressures, suggesting the presence of a biofilm between the skin and the surface. Fingerprints reduced contact area by a factor of one-third compared with flat skin, however, which would have reduced the friction; this casts severe doubt on their supposed frictional function.

That said, the author does later discuss their potential role in gripping of rough or wet surfaces:

So why do we have fingerprints? One possibility is that they increase friction on rougher surfaces compared with flat skin, because the ridges project into the depressions of such surfaces and provide a higher contact area. Experiments on materials of contrasting known roughness are needed to test this possibility.
A second possibility is that they facilitate runoff of water like the tread of a car tyre or grooves in the feet of tree frogs (Federle et al., 2006), so that they improve grip on wet surfaces. Though there is evidence that friction falls on fingers coated with high levels of moisture (Andre et al., 2008) it is possible that it falls less quickly on fingertips than on flatter skin. Once more, suitable experiments could test this idea.


There seems to be more consensus on the idea that fingerprints are useful for tactile sensation. The following are just some articles which discuss this.
Effect of fingerprints orientation on skin vibrations during tactile exploration of textured surfaces.

In humans, the tactile perception of fine textures is mediated by skin vibrations when scanning the surface with the fingertip. These vibrations are encoded by specific mechanoreceptors, Pacinian corpuscules (PCs), located about 2 mm below the skin surface. In a recent article, we performed experiments using a biomimetic sensor which suggest that fingerprints (epidermal ridges) may play an important role in shaping the subcutaneous stress vibrations in a way which facilitates their processing by the PC channel. Here we further test this hypothesis by directly recording the modulations of the fingerpad/substrate friction force induced by scanning an actual fingertip across a textured surface. When the fingerprints are oriented perpendicular to the scanning direction, the spectrum of these modulations shows a pronounced maximum around the frequency v/λ, where v is the scanning velocity and λ the fingerprints period. This simple biomechanical result confirms the relevance of our previous finding for human touch.

The role of fingerprints in the coding of tactile information probed with a biomimetic sensor.

In humans, the tactile perception of fine textures (spatial scale &lt;200 micrometers) is mediated by skin vibrations generated as the finger scans the surface. To establish the relationship between texture characteristics and subcutaneous vibrations, a biomimetic tactile sensor has been designed whose dimensions match those of the fingertip. When the sensor surface is patterned with parallel ridges mimicking the fingerprints, the spectrum of vibrations elicited by randomly textured substrates is dominated by one frequency set by the ratio of the scanning speed to the interridge distance. For human touch, this frequency falls within the optimal range of sensitivity of Pacinian afferents, which mediate the coding of fine textures. Thus, fingerprints may perform spectral selection and amplification of tactile information that facilitate its processing by specific mechanoreceptors.

This paper also asserts a reason for the elliptical nature of fingerprints:

In humans, fingerprints are organized in elliptical twirls so that each region of the fingertip (and thus each PC) can be ascribed with an optimal scanning orientation.