If the θ=∞ conjecture holds for automorphic L-functions, then they are non-vanishing in certain critical strip regions and families satisfy a quasi-Riemann Hypothesis.
Limitations to mollifying $\zeta(s)$
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abstract
We establish limitations to how well one can mollify the Riemann zeta-function on the critical line with mollifiers of arbitrary length. Our result gives a non-trivial lower bound for the contribution of the off-diagonal terms to mollified moments of \zeta(s). On the Riemann Hypothesis, we establish a connection between the mollified moment and Montgomery's Pair Correlation Function.
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2026 1verdicts
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The $\theta = \infty$ Conjecture and the Riemann Hypothesis for Automorphic $L$-functions
If the θ=∞ conjecture holds for automorphic L-functions, then they are non-vanishing in certain critical strip regions and families satisfy a quasi-Riemann Hypothesis.