Related papers: Primitive forms for Gepner singularities

We discuss properties of the Seifert form for simple $K3$ singularities, and of the Picard lattices of families of weighted $K3$ surfaces. We study a collection $\mathcal{M}_{(\rho,\,\delta)}$ of $K3$ surfaces polarized by their Picard…

Let $G_n$ denote either the group $SO(2n+1, F)$, $Sp(2n, F)$, or $GSpin(2n+1, F)$ over a non-archimedean local field of characteristic different than two. We determine all composition factors of degenerate principal series of $G_n$, using…

The problem of simplicity of Fermat number-twins $f_{n}^{\pm}=2^{2^n}\pm3$ is studied. The question for what $n$ numbers $f_{n}^{\pm}$ are composite is investigated. The factor-identities for numbers of a kind $x^2 \pm k $ are found.

Let $k$ be a field and let $R$ be a countable dimensional prime von Neumann regular $k$-algebra. We show that $R$ is primitive, answering a special case of a question of Kaplansky.

We construct highly singular projective curves and surfaces defined by invariants of primitive complex reflection groups.

"Fusion rules" are laws of multiplication among eigenspaces of an idempotent. This terminology is relatively new and is closely related to primitive axial algebras, introduced recently by Hall, Rehren, and Shpectorov. Axial algebras, in…

Many invariants of finitely generated positive cancelative commutative semigroups can be studied from their Poincar\'e series. We offer and present several closed formulas for them. Moreover, those formulas have elementary proofs and are…

We prove that equivariantly simple invariant singularities can only exist for very few representations of a group of prime order: for real representations and some ``almost, but not quite real'' representations.

Let $G$ be a finite primitive permutation group on a set $\Omega$ with nontrivial point stabilizer $G_{\alpha}$. We say that $G$ is extremely primitive if $G_{\alpha}$ acts primitively on each of its orbits in $\Omega \setminus \{\alpha\}$.…

In order to construct the inverse mapping of the period mapping for the primitive form for the semi-universal deformation of a simple elliptic singularity, K.Saito introduced in [5] the ``flat structure'' for the extended affine root…

We define a variant of Benjamini-Schramm convergence for finite simplicial complexes with the action of a fixed finite group G which leads to the notion of random rooted simplicial G-complexes. For every random rooted simplicial G-complex…

Working in a theory with an integer-valued dimension on interpretable sets, we classify pseudofinite definably primitive permutation groups acting on one-dimensional sets which satisfy a version of chain condition on centralizers and on…

The purpose of this note is to extend the classical Aschbacher--O'Nan--Scott theorem for finite groups to the class of countable linear groups. This relies on the analysis of primitive actions carried out in a previous paper. Unlike the…

Extending a classical estimate of Mertens for the sum of the reciprocals of the first primes, we provide an explicit remainder formula for products of an arbitrary, but fixed, number of primes.

We unify and generalize formulas obtained by Campillo, Delgado and Gusein-Zade in their series of articles. Positive results are established for rational and minimally elliptic singularities. By examples and counterexamples we also try to…

We introduce the primitivity of Fricke families, and give some examples. As its application, we first construct generators of the function field of the modular curve of level $N$ in terms of Fricke functions and Siegel functions,…

We consider the sums of the form $$ S=\sum_{x=1}^{N} \exp\big((ax+b_1g_1^x+... +b_rg_r^x)/p \big) $$, where $p$ is prime and $g_1,..., g_r$ are primitive roots $\pmod p$. An almost forty years old problem of L. J. Mordell asks to find a…

Let $\phi$ denote a primitive Hecke-Maass cusp form for $\Gamma_o(N)$ with the Laplacian eigenvalue $\lambda_\phi=1/4+t_{\phi}^2$. In this work we show that there exists a prime $p$ such that $p\nmid N$, $|\alpha_{p}|=|\beta_{p}| = 1$, and…

We introduce so-called cone topologies of paratopological groups, which are a wide way to construct counterexamples, especially of examples of compact-like paratopological groups with discontinuous inversion. We found a simple interplay…

We study the asymptotic behaviour of polarization form in the variation of mixed Hodge structure associated to isolated hypersurface singularities. The contribution characterizes a modification of Grothendieck residue as the polarization on…