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In this paper we consider the problem of approximating frequency moments inthe streaming model. Given a stream $D = \{p_1,p_2,\dots,p_m\}$ of numbers from$\{1,\dots, n\}$, a frequency of $i$ is defined as $f_i = |\{j: p_j = i\}|$.The $k$-th \emph{frequency moment} of $D$ is defined as $F_k = \sum_{i=1}^nf_i^k$.  In this paper we give an upper bound on the space required to find a $k$-thfrequency moment of $O(n^{1-2/k})$ bits that matches, up to a constant factor,the lower bound of Woodruff and Zhang (STOC 12) for constant $\epsilon$ andconstant $k$. Our algorithm makes a single pass over the stream and works forany constant $k > 3$.

Approximating Large Frequency Moments with $O(n^{1-2/k})$ Bits