Abstract
Let L k denote the Lebesgue constants of the Walsh system. The following exact result is established by means of Mellin transforms: ∑ 1≤k<n Lk= n 4 log 2n+nF( log 2n)− L n 2 forn⩾1 where F( u) is a continuous periodic function with period 1 whose Fourier coefficients can be explicitly expressed in terms of Riemann's zeta function. This improves an old result of Fine.
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