Related papers: Differential modules on p-adic polyannuli
In this paper we study special bases of certain spaces of half-integral weight weakly holomorphic modular forms. We establish a criterion for the integrality of Fourier coefficients of such bases. By using recursive relations between Hecke…
Recent decades have provided a host of examples and applications motivating the study of nonlocal differential operators. We discuss a class of such operators acting on bounded domains, focusing on those with integrable kernels having…
We estimate the fraction of isogeny classes of abelian varieties over a finite field which have a given characteristic polynomial P(T) modulo l. As an application we find the proportion of isogeny classes of abelian varieties with a…
Let $k$ be an infinite field of positive characteristic. We determine all homomorphisms between Weyl modules for $GLn(k)$, where one of the partitions is a hook. As a consequence we obtain a nonvanishing result concerning homomorphisms…
Let $\mathcal{R}$ be a free Lie conformal algebra of rank $2$ with $\mathbb{C}[\partial]$-basis $\{L,I\}$ and relations \begin{eqnarray*} \left[L_{\lambda} L\right]=(\partial+2 \lambda) (L+I),\ \left[L_{\lambda} I\right]=(\partial+\lambda)…
The Kreck-Stolz s invariant is used to distinguish connected components of the moduli space of positive scalar curvature metrics. We use a formula of Kreck and Stolz to calculate the s invariant for metrics on S^n bundles with nonnegative…
We discuss asymptotic properties of a family of discrete probability measures which may be used to model particle configurations with a wall on a set of discrete nodes. The correlations are shown to be determinantal and are expressed in…
Guided by the $Q$-shaped derived category framework introduced by Holm and Jorgensen, we provide a differential module analogue of a classical result that characterises when a finitely generated module over a local commutative noetherian…
We solve the problem of constructing all chiral genus-one correlation functions from chiral genus-zero correlation functions associated to a vertex operator algebra satisfying the following conditions: (i) the weight of any nonzero…
This text is a draft of the review paper on projectively dual varieties. Topics include dual varieties, Pyasetskii pairing, discriminant complexes, resultants and schemes of zeros, secant and tangential varieties, Ein theorems, applications…
In this article, we study the nature of zeros of weakly holomorphic modular forms. In particular, we prove results about transcendental zeros of modular forms of higher levels and for certain Fricke groups which extend a work of Kohnen.…
Fix a manifold M, and let V be an infinite dimensional Lie algebra of vector fields on M. Assume that V contains a finite dimensional semisimple maximal subalgebra A, the projective or conformal subalgebra. A projective or conformal…
Differential properties for orthogonal polynomials in several variables are studied. We consider multivariate orthogonal polynomials whose gradients satisfy some quasi--orthogonality conditions. We obtain several characterizations for these…
Period polynomials have long been fruitful tools for the study of values of $L$-functions in the context of major outstanding conjectures. In this paper, we survey some facets of this study from the perspective of Eichler cohomology. We…
Recently, D. S. Kim and T. Kim have studied applications of um- bral calculus associated with p-adic invariant integrals on Zp (see [6]). In this paper, we investigate some interesting properties arising from umbral calculus. These…
This paper is devoted to the horizontal (``characteristic'') cohomology of systems of differential equations. Recent results on computing the horizontal cohomology via the compatibility complex are generalized. New results on the Vinogradov…
For a non-archimedean local field $F$ and a connected reductive group $G$ over $F$ equipped with a parabolic subgroup $P$, we show that the dualizing complex on $\mathrm{Bun}_P$, the moduli stack of $P$-bundles on the Fargues--Fontaine…
The goal of this paper is to show a (derived) $p$-adic Simpson correspondence for (locally) unipotent coefficients on smooth rigid-analytic varieties. Our results depend on a deformation to $\mathbf{B}_\mathtt{dr}^+/\xi^2$, and not on a…
Differential analysis aims at inferring global properties of nonlinear behaviors from the local analysis of the linearized dynamics. The paper motivates and illustrates the use of differential analysis on the nonlinear pendulum model, an…
We define extensions of the $L^2$-analytic invariants of closed manifolds, called delocalized $L^2$-invariants. These delocalized invariants are constructed in terms of a nontrivial conjugacy class of the fundamental group. We show that in…