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A New p-adic Method for Proving Irrationality and Transcendence Results
Jean-Paul Bezivin and Philippe Robba
Annals of Mathematics
Second Series, Vol. 129, No. 1 (Jan., 1989), pp. 151-160
Published by: Annals of Mathematics
Stable URL: http://www.jstor.org/stable/1971488
Page Count: 10
You can always find the topics here!Topics: Algebra, Coefficients, Rational functions, Mathematical theorems, Power series coefficients, Polynomials, Integers, Radii of convergence, Differential equations, Diameters
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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.
Annals of Mathematics © 1989 Annals of Mathematics