We study the amplitude of mesoscopic Aharonov-Bohm oscillations in quasi-one-dimensional (Q1D) diffusive rings. We consider first the lowtemperature limit of a fully coherent sample. The variance of oscillation harmonics is calculated as a function of the length of the leads attaching the ring to reservoirs. We further analyze the regime of relatively high temperatures, when the dephasing due to electron-electron interaction suppresses substantially the oscillations. We show that the dephasing length L AB φ governing the damping factor exp(−2πR/L AB φ) of the oscillations is parametrically different from the common dephasing length for the Q1D geometry. This is due to the fact that the dephasing is governed by energy transfers determined by the ring circumference 2πR, making L AB
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