Abstract
We will prove the following theorem on Walsh series, and we will derive from this theorem an effective and constructive method for the numerical integration of Walsh series by number-theoretic methods. Further, concrete computer calculations are given. Theorem. For base b > 2, dimension s > 1, and o > 1, c > 0 {b, s € N; c, a e R), let i,E~°(c) be the class of all functions f: (0, l)s -» C which are representable by absolutely convergent Walsh series to base b with Walsh coefficients W(h\,... ,hs) with the following property: \W(h\,... , hs) 2, provided that a > 1 + s/,, where
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