A NONVANISHING LEMMA FOR CERTAIN PADE APPROXIMATIONS OF THE SECOND KIND

作者：Merila Ville^*

来源：International Journal of Number Theory, 2011, 7(8): 1977-1997.

DOI：10.1142/S1793042111004964

• Generalized hypergeometric and q-hypergeometric functions
• explicit Pade approximations of the second kind
• nonvanishing lemma
• generalized Vandermonde determinant
• linear independence measure
• algebraic number field
• valuation

We prove the nonvanishing lemma for explicit second kind Pade approximations to generalized hypergeometric and q-hypergeometric functions. The proof is based on an evaluation of a generalized Vandermonde determinant. Also, some immediate applications to the Diophantine approximation is given in the form of sharp linear independence measures for hypergeometric E- and G-functions in algebraic number fields with different valuations.

• 出版日期2011-12