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OP-12075Number theoryOpen

Selberg congruence spectral-gap constant ( $C_{61}$ )

Selberg congruence spectral-gap constant: determine C 61 or improve its bounds; the repository records 0 (lower) and frac 7 64 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12068Number theoryOpen

$\mathrm{GL}_2$ Ramanujan conjecture exponent ( $C_{56}$ )

mathrm GL 2 Ramanujan conjecture exponent: determine C 56 or improve its bounds; the repository records 0 (lower) and tfrac 7 64 =0.109375 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026