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Given a quantum observable and a state, one can construct a classical observable, such that it is the optimal estimate of the quantum observable, in the sense of minimum variance. We demonstrate how t...
Motivic complexes and special values of zeta functions     zeta functions  Motivic complexes       font style='font-size:12px;'> 2015/12/10
Beginning with the conjecture of Artin and Tate in 1966, there has been a series of successively more general conjectures expressing the special values of the zeta function of an algebraic variety o...
The p-cohomology of an algebraic variety in characteristic p lies naturally in the category Db c .R/ of coherent complexes of graded modules over the Raynaud ring (Ekedahl-Illusie-Raynaud). We stu...
Integral Motives and Special Values of Zeta Functions     Zeta Functions  Integral Motives       font style='font-size:12px;'> 2015/12/10
For each ˉeld k, we deˉne a category of rationally decomposed mixed motives with Z-coe±cients. When k is ˉnite, we show that the category is Tannakian, and we prove formulas relating the behaviour of...
On asymptotic values of canonical Hecke L-functions     Character  evidence  masri       font style='font-size:12px;'> 2015/8/25
We derive an asymptotic for the rst moment of Hecke L-series associated to canonical qua- dratic characters. This provides another proof and slightly generalizes recent results by Masri and Kim-Masri...
We consider large-scale studies in which there are hundreds or thousands of correlated cases to investigate, each represented by its own normal variate, typically a z-value. A familiar example is pro...
The ith singular value of a transfer matrix need not be a differentiable function of frequency where its multiplicity is greater than one. We show that near a local maximum, however, the largest singu...
This document derives several expected values related to the parameterized mean model with Gaussian noise and their simplified forms.
Extremal values on the eccentric distance sum of trees     Eccentric distance sum  Domination number  Leaves  Bipartition       font style='font-size:12px;'> 2012/7/11
Let $G=(V_G, E_G)$ be a simple connected graph. The eccentric distance sum of $G$ is defined as $\xi^{d}(G) = \sum_{v\in V_G}\varepsilon_{G}(v)D_{G}(v)$, where $\varepsilon_G(v)$ is the eccentricity o...
We consider the Mahler measure of the polynomial 1+x_1+x_2+x_3+x_4, which is the first case not yet evaluated explicitly. A conjecture due to F. Rodriguez-Villegas represents this Mahler measure as a ...
We consider in this paper the collection of near maxima of the discrete, two dimensional Gaussian free field in a box with Dirichlet boundary conditions. We provide a rough description of the geometry...
In the 1980s B\"ocherer formulated a conjecture relating the central values of the imaginary quadratic twists of the spin L-function attached to a Siegel modular form $F$ to the Fourier coefficients o...
We study multiple zeta values (MZVs) from the viewpoint of zeta-functions associated with the root systems which we have studied in our previous papers. In fact, the $r$-ple zeta-functions of Euler-Za...
We prove that any Mordell-Tornheim sum with positive integer arguments can be expressed as a rational linear combination of multiple zeta values of the same weight and depth. By a result of Tsumura, i...
Abstract: We introduce a family of L-series specialising to both L-series associated to certain Dirichlet characters over F_q[T] and to integral values of Carlitz-Goss zeta function associated to F_q[...

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