2,456 research outputs found
On the universal norm distribution
We introduce and study the universal norm distribution in this paper, which
generalizes the concepts of universal ordinary distribution and the universal
Euler system. We study the Anderson type resolution of the universal norm
distribution and then use this resolution to study the group cohomology of the
universal norm distribution.Comment: 18 pages; correct typos, minor changes in Section 2.1, Proposition
4.5 adde
Spectral sequences of universal distribution and Sinnott's index formula
We prove an abstract index formula about Sinnott's symbol between two
different lattices. We also develop the theory of the universal distribution
and predistribution in a double complex point of view. The theory of spectral
sequence is used to interpret the index formula and to analyze the cohomology
of the universal distribution. Combing these results, we successfully prove
Sinnott's index formula about the Stickelberger ideal. In addition, the {1,
-1}-cohomology groups of the universal distribution and the universal
predistribution are obtained.Comment: 23 page
The universal Kolyvagin recursion implies the Kolyvagin recursion
let U_z be the universal norm distribution and M a fixed power of prime p, by
using the double complex method employed by Anderson, we study the universal
Kolyvagin recursion occurred in the canonical basis in the zero-th cohomology
group of U_z/M U_z. We furthermore show that the universal Kolyvagin recursion
implies the Kolyvagin recursion in the theory of Euler systems(cf. Theorem
4.5.4 of K. Rubin's book Euler systems). One certainly hopes this could lead a
new way to find new Euler systems.Comment: 14 page
On a conjecture of Wan about limiting Newton polygons
We show that for a monic polynomial over a number field containing
a global permutation polynomial of degree as its composition factor, the
Newton Polygon of does not converge for
passing through all finite places of . In the rational number field case,
our result is the "only if" part of a conjecture of Wan about limiting Newton
polygons
A Common Information-Based Multiple Access Protocol Achieving Full Throughput and Linear Delay
We consider a multiple access communication system where multiple users share
a common collision channel. Each user observes its local traffic and the
feedback from the channel. At each time instant the feedback from the channel
is one of three messages: no transmission, successful transmission, collision.
The objective is to design a transmission protocol that coordinates the users'
transmissions and achieves high throughput and low delay.
We present a decentralized Common Information-Based Multiple Access (CIMA)
protocol that has the following features: (i) it achieves the full throughput
region of the collision channel; (ii) it results in a delay that is linear in
the number of users, and is significantly lower than that of CSMA protocols;
(iii) it avoids collisions without channel sensing
Newton polygons of -functions of polynomials with
For prime and a power of , we obtain the slopes of
the -adic Newton polygons of -functions of with respect to finite characters when is larger
than an explicit bound depending only on and . The main tools are
Dwork's trace formula and Zhu's rigid transform theorem.Comment: 8 page
Linear complexity of generalized cyclotomic sequences of period
In this paper, we construct two generalized cyclotomic binary sequences of
period based on the generalized cyclotomy and compute their linear
complexity, showing that they are of high linear complexity when
Counting the solutions of
Given a polynomial , for every and , we study the number of
solutions of the congruence equation in such that for . We
deduce formulas and an algorithm to study for any prime
number and any integer. As consequences of our main results, we
completely solve: the counting problem of for any prime and any subset of ; the counting problem of
in the case for any and
, and the case general for any and satisfying
; the
counting problem of in the case
for any and any , and in the case general for any
and satisfying .Comment: 22 page
Signaling for Decentralized Routing in a Queueing Network
A discrete-time decentralized routing problem in a service system consisting
of two service stations and two controllers is investigated. Each controller is
affiliated with one station. Each station has an infinite size buffer.
Exogenous customer arrivals at each station occur with rate . Service
times at each station have rate . At any time, a controller can route one
of the customers waiting in its own station to the other station. Each
controller knows perfectly the queue length in its own station and observes the
exogenous arrivals to its own station as well as the arrivals of customers sent
from the other station. At the beginning, each controller has a probability
mass function (PMF) on the number of customers in the other station. These PMFs
are common knowledge between the two controllers. At each time a holding cost
is incurred at each station due to the customers waiting at that station. The
objective is to determine routing policies for the two controllers that
minimize either the total expected holding cost over a finite horizon or the
average cost per unit time over an infinite horizon. In this problem there is
implicit communication between the two controllers; whenever a controller
decides to send or not to send a customer from its own station to the other
station it communicates information about its queue length to the other
station. This implicit communication through control actions is referred to as
signaling in decentralized control. Signaling results in complex communication
and decision problems. In spite of the complexity of signaling involved, it is
shown that an optimal signaling strategy is described by a threshold policy
which depends on the common information between the two controllers; this
threshold policy is explicitly determined
A note on cyclotomic Euler systems and the double complex method
In this note we give the Kolyvagin recursion in cyclotomic Euler systens a
new and universal interpretation with the help of the double complex method
introduced by Anderson and further developed by Das and Ouyang. Namely, we show
that the recursion satisfied by Kolyvagin classes is the specialization of a
universal recursion independent of the chosen field satisfied by universal
Kolyvagin classes in the group cohomology of the universal ordinary
distribution a la Kubert. Further, we show by a method involving a variant of
the diagonal shift operation introduced by Das that certain group cohomology
classes belonging (up to sign) to a basis previously constructed by Ouyang also
satisfy the universal recursion.Comment: 17 page
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