Cellular networks employ a specific radio resource management policy distinguishing them from wired and Wi-Fi networks. A lack of awareness of this important mechanism potentially leads to resource-inefficient mobile applications. We perform the first network-wide, large-scale investigation of a particular type of application traffic pattern called periodic transfers where a handset periodically exchanges some data with a remote server every t seconds. Using packet traces containing 1.5 billion packets collected from a commercial cellular carrier, we found that periodic transfers are very prevalent in today's smartphone traffic. However, they are extremely resource-inefficient for both the network and enduser devices even though they predominantly generate very little traffic. This somewhat counter-intuitive behavior is a direct consequence of the adverse interaction between such periodic transfer patterns and the cellular network radio resource management policy. For example, for popular smartphone applications such as Facebook, periodic transfers account for only 1.7% of the overall traffic volume but contribute to 30% of the total handset radio energy consumption. We found periodic transfers are generated for various reasons such as keep-alive, polling, and user behavior measurements. We further investigate the potential of various traffic shaping and resource control algorithms. Depending on their traffic patterns, applications exhibit disparate responses to optimization strategies. Jointly using several strategies with moderate aggressiveness can eliminate almost all energy impact of periodic transfers for popular applications such as Facebook and Pandora.