PreprintCC BY-NC-ND 4.0arXiv
Recovering Dirichlet coefficients from even samples
Abstract
In this work, we determine the exact case error for recovering a Dirichlet coefficient from finitely many positive even samples with bounded additive errors. For sequences with a bounded tail and an unrestricted initial block, a polynomial estimator is minimax among all recovery maps. Its tail and noise constants admit explicit product formulas. We prove a sharp tail asymptotic on the index scale K^(3/2) and give a terminating procedure for selecting the sample count from a computable error bound.
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BibTeX
@misc{danesh2026recovering,
title = {{Recovering Dirichlet coefficients from even samples}},
author = {Payam Danesh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24174},
eprint = {2610.24174},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24174},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Recovering Dirichlet coefficients from even samples
AU - Payam Danesh
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.24174
UR - https://arxiv.org/abs/2610.24174
AB - In this work, we determine the exact case error for recovering a Dirichlet coefficient from finitely many positive even samples with bounded additive errors. For sequences with a bounded tail and an unrestricted initial block, a polynomial estimator is minimax among all recovery maps. Its tail and noise constants admit explicit product formulas. We prove a sharp tail asymptotic on the index scale K^(3/2) and give a terminating procedure for selecting the sample count from a computable error bound.
ER -