Related papers: Degree 1 elements of the Selberg class

Extending the method of Part I (alg-geom/9704004), we give recursive formulae for: the genus-1 Severi degree (formula first found by Getzler), the degree of the variety of 1-cuspidal curves of genus 0 or 1, and the linear (sectional)…

We construct a countable simple theory which, in Keisler's order, is strictly above the random graph (but "barely so") and also in some sense orthogonal to the building blocks of the recently discovered infinite descending chain. As a…

We construct a graph of Kummer elements in a given cyclic algebra of prime degree and study its properties. In case of degree 5, we provide sufficient conditions for two elements to have a chain of Kummer elements connecting them, such that…

We introduce and study the class of spherically ordered groups. The notions of spherically ordered groups and their spectra of spherical orderability are introduced. Values of these spectra are found for a series of natural groups.

A careful exposition of Zilber's quasiminimal excellent classes and their categoricity is given, leading to two new results: the L_w1,w(Q)-definability assumption may be dropped, and each class is determined by its model of dimension…

We obtain a complete classification of minimal simple unitary $W$-algebras.

In this paper, we define an ordering relation for a set of complex numbers, and research the properties and theorems of the ordering, solve some simple complex inequalities with the ordering.

The classical Selberg integral contains a power of the Vandermonde determinant. When that power is a square, it is easy to prove Selberg's identity by interpreting it as a determinant of one-variable integrals. We give similar proofs of…

Every endofunctor of the category of classes is proved to be set-based in the sense of Aczel and Mendler, therefore, it has a final coalgebra. Other basic properties of these endofunctors are proved, e.g. the existence of a free completely…

We introduce a class of group-like objects and prove that Cayley Theorem on groups has a counterpart in the class of group-like objects.

We prove a categorification of the stable elements formula of Cartan and Eilenberg. Our formula expresses the derived category and the stable module category of a group as a bilimit of the corresponding categories for the $p$-subgroups.

We give a short proof of the trace formula for Hecke operators on modular forms for the modular group, using the action of Hecke operators on the space of period polynomials.

We give an elementary and self-contained proof of the equivalence of a collection of Wolstenholme-type congruences due to Helou and Terjanian.

We prove some theorems which give sufficient conditions for the existence of prime numbers among the terms of a sequence which has pairwise relatively prime terms.

The d-Segal conditions of Dyckerhoff and Kapranov are exactness properties for simplicial objects based on the geometry of cyclic polytopes in d-dimensional Euclidean space. 2-Segal spaces are also known as decomposition spaces, and most…

A beautiful degree formula for the Grothendieck polynomials was recently given by Pechenik, Speyer, and Weigandt (2021). We provide an alternative proof of their degree formula, utilizing the climbing chain model for Grothendieck…

In a recent paper by L. Fel two new identities for the degree of syzygies are given. We present an algebraic proof of them, using only basic homological algebra tools. We also extend these results.

Necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a k-connected simple graph are detailed. Conditions are also given under which such a sequence is necessarily k-connected.

Let G be a simple algebraic group over an algebraically closed field k. We classify the spherical conjugacy classes of G.

A type analysable in one-based types in a simple theory is itself one-based.