For an integer p≥ 2 , let {xn}n∈N⊂T be the p-adic van der Corput sequence. For intervals [0 , α) ⊂ T and for positive integers N, consider the geometrically-shifted discrepancy function Dp,N,α(t)=∑n=0N-1X[0,α)(xn+t)-Nα. In this paper, we give a characterization of the asymptotic behavior of ‖Dp,N,α(·)‖L2(T) for N→ ∞ that depends on the p-adic expansion of α.
On the distribution of the van der Corput sequences / Beretti, T.. - In: ARCHIV DER MATHEMATIK. - ISSN 0003-889X. - 120:3(2023), pp. 283-295. [10.1007/s00013-022-01811-4]
On the distribution of the van der Corput sequences
Beretti, Thomas
2023-01-01
Abstract
For an integer p≥ 2 , let {xn}n∈N⊂T be the p-adic van der Corput sequence. For intervals [0 , α) ⊂ T and for positive integers N, consider the geometrically-shifted discrepancy function Dp,N,α(t)=∑n=0N-1X[0,α)(xn+t)-Nα. In this paper, we give a characterization of the asymptotic behavior of ‖Dp,N,α(·)‖L2(T) for N→ ∞ that depends on the p-adic expansion of α.File in questo prodotto:
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