We prove asymptotics and study sign patterns for coefficients in expansions of elements in the Habiro ring which satisfy a strange identity. As an application, we prove asymptotics and discuss positivity for the generalized ...

We study various self-adjoint realizations of the X-ray transform on the Euclidean disk D, obtained by considering specific singularly weighted L2 topologies. We first recover the well-known Singular Value Decompositions ...

We consider two sequences a(n) and b(n), 1≤n<∞, generated by Dirichlet series of the forms ∑n=1∞a(n)λsnand∑n=1∞b(n)μsn, satisfying a familiar functional equation involving the gamma function Γ(s). A general identity is ...

The study of the edge ideal I(DG) of a weighted oriented graph DG with underlying graph G started in the context of Reed-Muller type codes. We generalize a Cohen-Macaulay construction for I(DG), which Villarreal gave for ...

We obtain a three-parameter q-series identity that generalizes two results of Chan and Mao. By specializing our identity, we derive new results of combinatorial significance in connection with N(r,s,m,n), a function counting ...

Modular forms on the split exceptional group G2 over Q are a special class of automorphic forms on this group, which were introduced by Gan, Gross, and Savin. If π is a cuspidal automorphic representation of G2(A) corresponding ...

In this article, we prove that a tame twisted K3 surface over an algebraically closed field of positive characteristic has only finitely many tame twisted Fourier-Mukai partners and we give a counting formula in case we ...

In this article, we study special values of the Dedekind zeta function over an imaginary quadratic field. The values of the Dedekind zeta function at any even integer over any totally real number field is quite well known ...