@article {IOPORT.05131431,
    author       = {Liu, Huaning},
    title        = {New pseudorandom sequences constructed by quadratic residues and Lehmer numbers.},
    year         = {2007},
    journal      = {Proceedings of the American Mathematical Society},
    volume       = {135},
    number       = {5},
    issn         = {0002-9939},
    pages        = {1309-1318},
    publisher    = {American Mathematical Society, Providence, RI},
    doi          = {10.1090/S0002-9939-06-08630-8},
    abstract     = {The author considers the sequence $$e_n=\cases (-1)^{n+\bar{n}}\ ,& \text{if}\ n\ \text{is QR }\mod p\\ (-1)^{n+\bar{n}+1}\ ,&\text{if}\ n\ \text{is not QR }\mod p\ , \endcases$$ where $\bar{n}$ is the multiplicative inverse of $n\mod p$ such that $1\le\bar{n}\le p-1$ and QR means quadratic residue. Following a series of papers of Mauduit and Sark\H{o}zy et al., the author studies the well distribution measure $W_{p-1}$ of the sequence $\{e_1,\ldots,e_{p-1}\}$ the pair-correlation measure $C_{p-1}$ and a combined well-distribution-correlation measure. These measures are useful quantities to describe the distribution behavior of the pseudorandom sequence $(e_n)^{p-1}_{n=1}$. The main theorem gives upper bounds for these measures, for instance $W_{p-1}\ll p^{1/2}\log^2 p$ and $C_{p-1}\ll p^{1/2}\log^3p$. The proofs essentially depend on a detailed analysis of Kloosterman sums.},
    reviewer     = {Robert F. Tichy (Graz)},
    identifier   = {05131431},
}