Canadian Journal of Mathematics
The solvability for a nonlinear degenerate hyperbolic–parabolic coupled system arising from nematic liquid crystals
This paper focuses on the Cauchy problem for a one-dimensional quasilinear hyperbolic–parabolic coupled system with initial data given on a line of parabolicity. The coupled system is derived from the Poiseuille flow of full Ericksen–Leslie model in th…
Canadian Journal of Mathematics
Lambert series of logarithm, the derivative of Deninger’s function $R(z),$ and a mean value theorem for $\zeta \left (\frac {1}{2}-it\right )\zeta ‘\left (\frac {1}{2}+it\right )$
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…
Canadian Journal of Mathematics
Asymptotics for symmetrized positive moments of odd ranks
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…
Canadian Journal of Mathematics
Weighted nonlinear flag manifolds as coadjoint orbits
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…
Canadian Journal of Mathematics
The Kudla–Millson form via the Mathai–Quillen formalism
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…
Canadian Journal of Mathematics
Tensor algebras of subproduct systems and noncommutative function theory
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…
Canadian Journal of Mathematics
Examples of dHYM connections in a variable background
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…
Canadian Journal of Mathematics
Shifted moments of the Riemann zeta function
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…
Canadian Journal of Mathematics
On some multiplicative properties of large difference sets
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…