Also appears in collection : 2018 - T1 - WS2 - Model theory and valued fields

In the middle of the 90’s Tate and Voloch have proved a result concerning the sums of roots of unity with fixed coefficients. By using an adapted decomposition to understand the p-adic valuation of these sums we will see how to improve their result and using it to axiomatize the valued structure Cp with a predicate for the group of roots of unity.