CARLO VIOLA

The arithmetic of Euler's integrals


Pages: 119-149
Received: 7 September 2004   
Mathematics Subject Classification (2000): 11J82 - 14E05 - 20B35 - 33C60

Abstract: We define double and triple Euler-type integrals generalizing the integrals considered by Beukers in 1979. We show how the permutation group method, recently introduced by Rhin and the author, applies to such integrals to yield the best known irrationality measures of z(2) and z(3). In the last section we introduce a family of 32 three-dimensional birational transformations changing integrals of Sorokin's type into integrals of Beukers' type. Such a family includes a transformation recently given by Fischler