Packet 2: Tossup 6

Description acceptable. This set’s existence restricts the behavior of functions in Voronin’s universality theorem. No values of this set exist in “free” regions bounded by the Vinogradov–Korobov theorem. The conjecture that certain values in this set’s (-5[1])generalizations do not exist was claimed to be proven in 2022 by Yitang Zhang. Subsets (-5[1])of this set on a bounded interval (10[1])have cardinalities (10[1]-5[1])bounded by the von Mangoldt formula. (-5[2])Generalizations of this set may possess “exceptional” values named for Siegel, (10[1]-5[1])which would refute a conjecture (10[1])for Dirichlet (10[2])L-functions. This set is summed over in an exact formula for the prime-counting (10[1])function. In contrast to the negative even integers, this set lies within a “critical strip.” (10[2])For 10 points, name this set in the complex plane (10[1])whose values are hypothesized (10[1])to all have real part one-half by (10[2])a (10[1])Millennium Prize (-5[1])problem. (10[1])■END■ (10[4]0[6])

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