Related papers: A remark on the geometric Jacquet functor
We demonstrate the generation of the three-dimensional Chern-Simons-like Lorentz-breaking ``mixed" quadratic action via an appropriate Lorentz-breaking coupling of vector and scalar fields to the spinor field and study some features of the…
An expression in the form of an easily computed integral is given for the determinant of the scalar GJMS operator on an odd--dimensional sphere. Manipulation yields a sum formula for the logdet in terms of the logdets of the ordinary…
We define Hecke operators on vector valued modular forms transforming with the Weil representation associated to a discriminant form. We describe the properties of the corresponding algebra of Hecke operators and study the action on modular…
We consider analogs of Jacobson's $F$-Burnside construction and Boltje's $(-)_+$-construction for biset functors, using Mackey-functor theoretic interpretation of biset functors.
Beginning from the resolution of the Dirichlet L function, using the inner product formula between two infinite-dimensional vectors in the complex space, the author proved the baffling problem--Hecke conjecture.
In this paper we introduce a new approach to determinant functors which allows us to extend Deligne's determinant functors for exact categories to Waldhausen categories, (strongly) triangulated categories, and derivators. We construct…
J. R. Wilton obtained an expression for the product of two Riemann zeta functions. This expression played a crucial role to find the approximate functional equation for the product of two Riemann zeta functions in the critical region. We…
Jackson's q-exponential is expressed as the exponential of a series whose coefficients are obtained in closed form. Such a relation is used to derive some properties of the q-exponential.
The topological charge in the $\U(N)$ vector-like reduced model can be defined by using the overlap Dirac operator. We obtain its large $N$ limit for a fermion in a general gauge-group representation under a certain restriction of gauge…
This is a survey on rigidity and geometrization results obtained with the help of the discrete Hilbert-Einstein functional, written for the proceedings of the "Discrete Curvature" colloquium in Luminy.
In [Grenier-Nguyen], we introduced so called {\em generators} functions to precisely follow the regularity of analytic solutions of Navier Stokes equations. In this short note, we give a presentation of these generator functions and use…
We compute the second moment of the Dedekind zeta function of a quadratic field times an arbitrary Dirichlet polynomial of length $T^{1/11-\epsilon}$.
We propose the notion of the {\em crystalline sub-representation functor} defined on $p$-adic representations of the Galois groups of finite extensions of $\Qp$, with certain restrictions in the case of integral representations. By studying…
We compute the derived functors of the third symmetric-power functor and their cross-effects for certain values. These calculations match predictions by the first named author and largely prove them in general.
A Riemannian manifold endowed with $k>2$ orthogonal complementary distributions (called here a Riemannian almost $k$-product structure) appears in such topics as multiply warped products, the webs composed of several foliations, and proper…
We present a new recursion and Hamiltonian operators for the Viallet equation. This new recursion operator and the recursion operator found in [Theoretical and Mathematical Physics, 167:421--443 (2011), arXiv:1004.5346] satisfy the elliptic…
Elliptic functions considered by Dixon in the nineteenth century and related to Fermat's cubic, $x^3+y^3=1$, lead to a new set of continued fraction expansions with sextic numerators and cubic denominators. The functions and the fractions…
We give a geometric interpretation of the group law for Jacobian varieties by extending the geometric construction of chords and tangents on an elliptic curve. For any given algebraic curve $\mathcal X$ and reduced divisors $D_1, D_2 \in…
The Lie-Trotter formula $e^{\hat{A}+\hat{B}} = \lim_{N\to \infty} (e^{\hat{A}/N} e^{\hat{B}/N})^N$ is of great utility in a variety of quantum problems ranging from the theory of path integrals and Monte Carlo methods in theoretical…
This article describes a formula for second variation of generalized Einstein-Hilbert functional on Riemannian manifolds. This work extends the definition of stable Einstein manifolds, and we present some properties.