%0 Journal Article %T On the (LC) conjecture %A Mohsen Asgharzadeh %J Mathematics %D 2015 %I arXiv %X We prove the (LC) conjecture of Hochster and Huneke in a series of nontrivial cases. This has many facilities. Recently, Brenner and Caminata answered a numerical evidence due to Dao and Smirnov on the generalized Hilbert-Kunz functions. As a first application, we reprove this by a short argument. As a second application, we give a proof of another numerical evidence. Third, we answer a question posted by Vraciu. %U http://arxiv.org/abs/1512.02518v1