Does a PC antivirus software like avast detect mobile phone viruses?

Some anti-virus programs for the PC can detect mobile phone viruses ON THE PC - that is, before they have been transferred to the phone. However, for proper protection of the phone you need a phone-based anti-virus program.

Also note that it depends very much on your phone model. Some (most, actually) phone models cannot be infected and you don't need anti-virus software for them. You mainly need anti-virus software for mobile phones using the Symbian S60 R2 operating system (mostly the older models of Nokia smart phones). While proof-of-concept viruses also exist for devices running the PalmOS, Windows Mobile and Symbian UIQ operating systems, they have no chances of surviving in the wild. There are also no viruses for devices that use the Symbian S60 R3 operating system (mostly - the newer models of Nokia smart phones), since it is much more secure than the R2 version and is incompatible with the latter.

In particular, AVAST offer a mobile version of their anti-virus program - but only for devices running the PalmOS or Windows Mobile operating systems. Surprisingly, they don't offer a version for devices using the Symbian S60 R2 operating system - yet this is the environment which is the most threatened by mobile malware.

Does a PC antivirus software like avast detect mobile phone viruses?antivirus downloads

Nope.