Abstract
Using p-adic methods, we shall prove the Lindemann-Weierstrass Theorem: The values taken by the exponential function at different algebraic points are linearly independent over the field of algebraic numbers. Likewise we shall prove that if K is the field of rational numbers or an imaginary quadratic extension of Q, the values at different points of K of some special functions (for example the Bessel function) are linearly independent over K.
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