This content will become publicly available on July 4, 2023
 Award ID(s):
 2007959
 Publication Date:
 NSFPAR ID:
 10385968
 Journal Name:
 ISSAC'2022
 Page Range or eLocationID:
 111 to 118
 Sponsoring Org:
 National Science Foundation
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Abstract The zeta function of a curve C over a finite field may be expressed in terms of the characteristic polynomial of a unitary matrix Θ C . We develop and present a new technique to compute the expected value of tr(Θ C n ) for various moduli spaces of curves of genus g over a fixed finite field in the limit as g is large, generalising and extending the work of Rudnick [ Rud10 ] and Chinis [ Chi16 ]. This is achieved by using function field zeta functions, explicit formulae, and the densities of prime polynomials with prescribed ramification types at certain places as given in [ BDF + 16 ] and [ Zha ]. We extend [ BDF + 16 ] by describing explicit dependence on the place and give an explicit proof of the Lindelöf bound for function field Dirichlet L functions L (1/2 + it , χ). As applications, we compute the onelevel density for hyperelliptic curves, cyclic ℓcovers, and cubic nonGalois covers.

Molecular dynamics (MD) is a powerful tool for studying intrinsically disordered proteins, however, its reliability depends on the accuracy of the force field. We assess Amber ff19SB, Amber ff14SB, OPLSAA/M, and CHARMM36m with respect to their capacity to capture intrinsic conformational dynamics of 14 guest residues x (=G, A, L, V, I, F, Y, D P , E P , R, C, N, S, T) in GxG peptides in water. The MDderived Ramachandran distribution of each guest residue is used to calculate 5 Jcoupling constants and amide I′ band profiles to facilitate a comparison to spectroscopic data through reduced χ 2 functions. We show that the Gaussian model, optimized to best fit the experimental data, outperforms all MD force fields by an order of magnitude. The weaknesses of the MD force fields are: (i) insufficient variability of the polyproline II (pPII) population among the guest residues; (ii) oversampling of antiparallel at the expense of transitional βstrand region; (iii) inadequate sampling of turnforming conformations for ionizable and polar residues; and (iv) insufficient guest residuespecificity of the Ramachandran distributions. Whereas Amber ff19SB performs worse than the other three force fields with respect to χ 2 values, it accounts for residuespecific pPII contentmore »

ABSTRACT Many astrophysical environments, from star clusters and globular clusters to the discs of active galactic nuclei, are characterized by frequent interactions between stars and the compact objects that they leave behind. Here, using a suite of 3D hydrodynamics simulations, we explore the outcome of close interactions between $1\, \mathrm{M}_{\odot }$ stars and binary black holes (BBHs) in the gravitational wave regime, resulting in a tidal disruption event (TDE) or a pure scattering, focusing on the accretion rates, the back reaction on the BH binary orbital parameters, and the increase in the binary BH effective spin. We find that TDEs can make a significant impact on the binary orbit, which is often different from that of a pure scattering. Binaries experiencing a prograde (retrograde) TDE tend to be widened (hardened) by up to $\simeq 20{{\ \rm per\ cent}}$. Initially circular binaries become more eccentric by $\lesssim 10{{\ \rm per\ cent}}$ by a prograde or retrograde TDE, whereas the eccentricity of initially eccentric binaries increases (decreases) by a retrograde (prograde) TDE by $\lesssim 5{{\ \rm per\ cent}}$. Overall, a single TDE can generally result in changes of the gravitationalwavedriven merger timescale by order unity. The accretion rates of both black holesmore »

The Iwasawa theory of CM fields has traditionally concerned Iwasawa modules that are abelian prop Galois groups with ramification allowed at a maximal set of primes over p such that the module is torsion. A main conjecture for such an Iwasawa module describes its codimension one support in terms of a padic Lfunction attached to the primes of ramification. In this paper, we study more general and potentially much smaller modules that are quotients of exterior powers of Iwasawa modules with ramification at a set of primes over p by sums of exterior powers of inertia subgroups. We show that the higher codimension support of such quotients can be measured by finite collections of characteristic ideals of classical Iwasawa modules, hence by padic Lfunctions under the relevant CM main conjectures.

Abstract The elliptic algebras in the title are connected graded $\mathbb {C}$ algebras, denoted $Q_{n,k}(E,\tau )$ , depending on a pair of relatively prime integers $n>k\ge 1$ , an elliptic curve E and a point $\tau \in E$ . This paper examines a canonical homomorphism from $Q_{n,k}(E,\tau )$ to the twisted homogeneous coordinate ring $B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$ on the characteristic variety $X_{n/k}$ for $Q_{n,k}(E,\tau )$ . When $X_{n/k}$ is isomorphic to $E^g$ or the symmetric power $S^gE$ , we show that the homomorphism $Q_{n,k}(E,\tau ) \to B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$ is surjective, the relations for $B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$ are generated in degrees $\le 3$ and the noncommutative scheme $\mathrm {Proj}_{nc}(Q_{n,k}(E,\tau ))$ has a closed subvariety that is isomorphic to $E^g$ or $S^gE$ , respectively. When $X_{n/k}=E^g$ and $\tau =0$ , the results about $B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$ show that the morphism $\Phi _{\mathcal {L}_{n/k}}:E^g \to \mathbb {P}^{n1}$ embeds $E^g$ as a projectively normal subvariety that is a schemetheoretic intersection of quadric and cubic hypersurfaces.