We refine a bound of Cheng-Feyzbakhsh to prove an asymptotic $\Gamma$-Bayer-Macr\`i-Toda ($\Gamma$-BMT) inequality on every smooth polarized complex threefold. The proof relies on a reduction to small tilt stability parameters. Using this inequality we verify Feyzbakhsh-Thomas's condition $(wBG)$ whenever $K_{X}$ is numerically proportional to the polarization. For polarized Calabi-Yau threefolds, this yields a reduction of positive rank generalized Donaldson-Thomas (DT) invariants to those counting sheaves pure in codimension one. We further express these invariants in terms of rank one generalized DT invariants. Thus, the rank reductions of Feyzbakhsh-Thomas hold without assuming the BMT conjecture.
The Jensen--P\'olya criterion expresses the generalized Riemann hypothesis (GRH) for Dedekind zeta-functions as a real-rootedness condition on their Jensen polynomials. Previous asymptotic results require large shifts, while computations establish real-rootedness in the Riemann case through a finite range of degrees. H...
We prove Conjecture B of Akhtar--Coates--Corti--Heuberger--Kasprzyk--Oneto--Petracci--Prince--Tveiten unconditionally for the normalized family of maximally mutable Laurent polynomials with prescribed $T$-binomial edge coefficients associated with the degree-10 orbifold del Pezzo hypersurface $X_{10}\subset\mathbb{P}(1...
We prove the global Mizohata-Takeuchi estimate for bounded complexity weights in $\mathbb{R}^2$ and an arbitrary $C^2$ uniformly convex curve on the Fourier side, with an implied constant depending only on the complexity and the curve. A version with a logarithmic loss follows from a short argument using the $T^*T$ met...
We consider a family of non-local and non-convex functionals depending on three real parameters $(\gamma,p,\lambda)$, which was introduced by H. Brezis, A. Seeger, J. Van Schaftingen and P. L. Yung. In the case $\gamma<-p$ we prove a lower bound for the Gamma-liminf of these functionals as $\lambda\to 0^+$ and a Poinca...
We give $L^2$-bounds with respect to the height of the spectral parameter for Epstein zeta functions $\mathrm{Z}_Q(s)$ and non-holomorphic Eisenstein series $E_{\mathfrak{c}}(s,z)$ attached to the Hecke congruence subgroup $\Gamma_0 (p)$ of prime level $p$. Our bounds are completely explicit in the level and, additiona...
Motivated by a log-convexity question of Bennett and Tao, we consider Gowers-type functionals defined by $L^p$ norms of multiple autocorrelations. We prove sharp bounds in terms of $L^q$ norms and characterise the near-extremisers on Euclidean spaces as well as locally compact abelian groups. We also establish two fami...
Vjekoslav Kovač, K. Rogers· 1 citation· ⚡1
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