scholarly journals Harmonic analysis and statistics of the first Galois cohomology group

2021 ◽  
Vol 8 (3) ◽  
Author(s):  
Brandon Alberts ◽  
Evan O’Dorney
Keyword(s):  
Growth Rates ◽  
Tauberian Theorem ◽  
Cohomology Group ◽  
Galois Cohomology ◽  
Canonical Decomposition ◽  
New Techniques ◽  
Counting Problem ◽  
Asymptotic Growth ◽  
Generating Series ◽  
Euler Products

AbstractWe utilize harmonic analytic tools to count the number of elements of the Galois cohomology group $$f\in H^1(K,T)$$ f ∈ H 1 ( K , T ) with discriminant-like invariant $$\text {inv}(f)\le X$$ inv ( f ) ≤ X as $$X\rightarrow \infty $$ X → ∞ . Specifically, Poisson summation produces a canonical decomposition for the corresponding generating series as a sum of Euler products for a very general counting problem. This type of decomposition is exactly what is needed to compute asymptotic growth rates using a Tauberian theorem. These new techniques allow for the removal of certain obstructions to known results and answer some outstanding questions on the generalized version of Malle’s conjecture for the first Galois cohomology group.

Mappings on Decomposable Combinatorial Structures: Analytic Approach

2002 ◽  
Vol 11 (1) ◽  
pp. 61-78 ◽  
Author(s):  
E. MANSTAVIČIUS
Keyword(s):  
Number Theory ◽  
Generating Functions ◽  
Multiplicative Functions ◽  
Combinatorial Structures ◽  
Mean Values ◽  
Taylor Coefficients ◽  
Probabilistic Number ◽  
Generating Series ◽  
Euler Products ◽  
Complex Valued

On the class of labelled combinatorial structures called assemblies we define complex-valued multiplicative functions and examine their asymptotic mean values. The problem reduces to the investigation of quotients of the Taylor coefficients of exponential generating series having Euler products. Our approach, originating in probabilistic number theory, requires information on the generating functions only in the convergence disc and rather weak smoothness on the circumference. The results could be applied to studying the asymptotic value distribution of decomposable mappings defined on assemblies.

The two-stream instability and its classification into absolute and convective for hot plasmas

1970 ◽  
Vol 4 (3) ◽  
pp. 607-615 ◽  
Author(s):  
E. Infeld ◽  
A. Skorupski
Keyword(s):  
Growth Rates ◽  
Stability Limit ◽  
Asymptotic Growth ◽  
Convective Instabilities ◽  
The Stability ◽  
Stream Instability

This paper deals with the problem of classification of the two-stream instability for hot plasmas. The method is based on the criterion of Fainberg, Kurilko & Shapiro (1961). The basis of the analysis is the ‘resonance’ distribution, but a modified resonance distribution, leading to better results, is also investigated. The stability limit, classification into absolute and convective instabilities, as well as asymptotic growth rates are given for some chosen values of stream densities and temperatures, and arbitrary stream velocities. A method for finding the maximum temporal growth rates is also outlined.

On K2 of varieties over number fields

2008 ◽  
Vol 1 (1) ◽  
pp. 175-183
Author(s):  
Cristian D. González-Avilés
Keyword(s):  
Number Field ◽  
Cohomology Group ◽  
Complex Multiplication ◽  
Galois Cohomology ◽  
Number Fields ◽  
Chow Group ◽  
Torsion Subgroup ◽  
Vanishing Theorem ◽  
Finite Exponent ◽  
Torsion Free

AbstractLet k be a number field and let X be a smooth, projective and geometrically integral k-variety. We show that, if the geometric Néron-Severi group of X is torsion-free, then the Galois cohomology group is finite. Previously this group was only known to have a finite exponent. We also obtain a vanishing theorem for this group, showing in particular that it is trivial if X belongs to a certain class of abelian varieties with complex multiplication. The interest in the above cohomology group stems from its connection to the torsion subgroup of the Chow group CH2(X) of codimension 2 cycles on X. In the last section of the paper we record certain results on curves which must be familiar to all specialists in this area but which we have not formerly seen in print.

scholarly journals On the Galois Cohomology Group of the Ring of Integers in a Global Field and its Adele Ring

1968 ◽  
Vol 32 ◽  
pp. 247-252 ◽  
Author(s):  
Yoshiomi Furuta ◽  
Yasuaki Sawada
Keyword(s):  
Algebraic Number ◽  
Cohomology Group ◽  
Present Note ◽  
Algebraic Function ◽  
Galois Cohomology ◽  
Algebraic Number Field ◽  
Global Field ◽  
Constant Field ◽  
Algebraic Function Field ◽  
Ring Of Integers

By a global field we mean a field which is either an algebraic number field, or an algebraic function field in one variable over a finite constant field. The purpose of the present note is to show that the Galois cohomology group of the ring of integers of a global field is isomorphic to that of the ring of integers of its adele ring and is reduced to asking for that of the ring of local integers.

Extreme growth plasticity in the early branching sauropodomorph Massospondylus carinatus

2021 ◽  
Vol 17 (5) ◽  
Author(s):  
Kimberley E. J. Chapelle ◽  
Jennifer Botha ◽  
Jonah N. Choiniere
Keyword(s):  
South African ◽  
Growth Rates ◽  
Growth Pattern ◽  
Developmental Plasticity ◽  
Histological Change ◽  
Skeletal Growth ◽  
The South ◽  
Asymptotic Growth ◽  
High Degree

There is growing evidence of developmental plasticity in early branching dinosaurs and their outgroups. This is reflected in disparate patterns of morphological and histological change during ontogeny. In fossils, only the osteohistological assessment of annual lines of arrested growth (LAGs) can reveal the pace of skeletal growth. Some later branching non-bird dinosaur species appear to have followed an asymptotic growth pattern, with declining growth rates at increasing ontogenetic ages. By contrast, the early branching sauropodomorph Plateosaurus trossingensis appears to have had plastic growth, suggesting that this was the plesiomorphic condition for dinosaurs. The South African sauropodomorph Massospondylus carinatus is an ideal taxon in which to test this because it is known from a comprehensive ontogenetic series, it has recently been stratigraphically and taxonomically revised, and it lived at a time of ecosystem upheaval following the end-Triassic extinction. Here, we report on the results of a femoral osteohistological study of M. carinatus comprising 20 individuals ranging from embryo to skeletally mature. We find major variability in the spacing of the LAGs and infer disparate body masses for M. carinatus individuals at given ontogenetic ages, contradicting previous studies. These findings are consistent with a high degree of growth plasticity in M. carinatus .

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