Alzheimer's Disease - Input of Vitamin D With mEmantine Assay

Current treatments for Alzheimer's disease and related disorders (ADRD) are symptomatic and can only temporarily slow down ADRD. Future possibilities of care could rely on multi-target drugs therapies that address simultaneously several pathophysiological processes leading to neurodegeneration. We hypothesized that the combination of memantine with vitamin D could be neuroprotective in ADRD, thereby limiting neuronal loss and cognitive decline. The primary objective of this trial is to compare the effect after 24 weeks of the oral intake of vitamin D3 with the effect of a placebo on the evolution of cognitive performance in patients suffering from moderate ADRD and receiving memantine. The secondary objectives of the study are as follows: * To compare the effect after 12 weeks of the oral intake of vitamin D3 with the effect of a placebo on the evolution of cognitive performance in patients suffering from moderate ADRD and receiving memantine. * To compare the effect after 12 and 24 weeks of the oral intake of vitamin D3 with the effect of a placebo on the evolution of functional abilities in patients suffering from moderate ADRD and receiving memantine. * To compare the effect after 12 and 24 weeks of the oral intake of vitamin D3 with the effect of a placebo on the evolution of postural and gait performance in patients suffering from moderate ADRD and receiving memantine. * To determine the compliance to treatment and tolerance of the oral intake of vitamin D3 in patients suffering from moderate ADRD and receiving memantine.