An explicit transformation for the series , or equivalently, for Re, which takes y to , is obtained for the first time. This series transforms into a series containing the derivative of , a function studied by Christopher Deninger while obtaining an a…
In 2007, Andrews introduced Durfee symbols and k-marked Durfee symbols so as to give a combinatorial interpretation for the symmetrized moment function of ranks of partitions. He also considered the relations between odd Durfee symbols and the mock th…
A weighted nonlinear flag is a nested set of closed submanifolds, each submanifold endowed with a volume density. We study the geometry of Fréchet manifolds of weighted nonlinear flags, in this way generalizing the weighted nonlinear Grassmannians. Whe…
A crucial ingredient in the theory of theta liftings of Kudla and Millson is the construction of a -form on an orthogonal symmetric space, using Howe’s differential operators. This form can be seen as a Thom form of a real oriented vector bundle. We s…
We revisit tensor algebras of subproduct systems with Hilbert space fibers, resolving some open questions in the case of infinite-dimensional fibers. We characterize when a tensor algebra can be identified as the algebra of uniformly continuous noncomm…
We study deformed Hermitian Yang–Mills (dHYM) connections on ruled surfaces explicitly, using the momentum construction. As a main application, we provide many new examples of dHYM connections coupled to a variable background Kähler metric. These are s…
In this article, we prove that the Riemann hypothesis implies a conjecture of Chandee on shifted moments of the Riemann zeta function. The proof is based on ideas of Harper concerning sharp upper bounds for the th moments of the Riemann zeta function o…
In our paper, we study multiplicative properties of difference sets for large sets in the case of composite q. We obtain a quantitative version of a result of A. Fish about the structure of the product sets . Also, we show that the multiplicative cov…
For a bounded analytic function on the unit disk with , we consider the defect operators and of the Toeplitz operators and , respectively, on the weighted Bergman space . The ranges of and , written as and and equipped with appropriate inner pr…
If is an eigenvector for eigenvalue of a graph X and is an automorphism of X, then is also an eigenvector for . Thus, it is rather exceptional for an eigenvalue of a vertex-transitive graph to have multiplicity one. We study cubic vertex-transitive…