Modular squaring bounties === * $5,000—Prove that SUM requires depth c*log2(n) for c > 2. (That is, improve upon Kra70.) * $5,000—Prove that SUM reqiures depth 4*log2(n). (That is, prove the "reasonable hypothesis" on page 3.) * $5,000—Improve any constant in Theorem 2. * Improve upon the $2log_2(n)$ depth lower bound of SUM. * $5,000—Prove the conjecture that SUM requires depth $4log_2(n)$. Other ideas --- * $1,000—Disprove the conjecture that SUM requires depth $4log_2(n)$ * $5,000—Extending the average-case lower bounds (see page 20). * Best paper (too subjective?) * $3,000—Extending the results to the Chinese Remainder Representation (see page 20). * $3,000—Extending the results to the Ozturk representation (see page 20).