Regulators of an Infinite Family of the Simplest Quartic Function Fields

2017 ◽  
Vol 69 (3) ◽  
pp. 579-594 ◽  
Author(s):  
Jungyun Lee ◽  
Yoonjin Lee
Keyword(s):  
Lower Bound ◽  
Finite Field ◽  
Polynomial Ring ◽  
Function Fields ◽  
Infinite Family ◽  
Class Numbers ◽  
Explicit Criterion ◽  
Divisor Class ◽  
The Family

AbstractWe explicitly find regulators of an infinite family {Lm} of the simplest quartic function fields with a parameter m in a polynomial ring [t], where is the finite field of order q with odd characteristic. In fact, this infinite family of the simplest quartic function fields are subfields of maximal real subfields of cyclotomic function fields having the same conductors. We obtain a lower bound on the class numbers of the family {Lm} and some result on the divisibility of the divisor class numbers of cyclotomic function fields that contain {Lm} as their subfields. Furthermore, we find an explicit criterion for the characterization of splitting types of all the primes of the rational function field (t) in {Lm}.

A Lower Bound on the Number of Cyclic Function Fields With Class Number Divisible byn

2006 ◽  
Vol 49 (3) ◽  
pp. 448-463 ◽  
Author(s):  
Allison M. Pacelli
Keyword(s):  
Lower Bound ◽  
Class Number ◽  
Function Fields ◽  
Quadratic Function ◽  
Class Numbers ◽  
Prime Degree ◽  
Cyclic Function ◽  
Quadratic Function Fields

AbstractIn this paper, we find a lower bound on the number of cyclic function fields of prime degreelwhose class numbers are divisible by a given integern. This generalizes a previous result of D. Cardon and R. Murty which gives a lower bound on the number of quadratic function fields with class numbers divisible byn.

scholarly journals A GENERALIZATION OF ROTH'S THEOREM IN FUNCTION FIELDS

2009 ◽  
Vol 05 (07) ◽  
pp. 1149-1154 ◽  
Author(s):  
YU-RU LIU ◽  
CRAIG V. SPENCER
Keyword(s):  
Finite Field ◽  
Polynomial Ring ◽  
Trivial Solution ◽  
Function Fields

Let 𝔽q[t] denote the polynomial ring over the finite field 𝔽q, and let [Formula: see text] denote the subset of 𝔽q[t] containing all polynomials of degree strictly less than N. For non-zero elements r1, …, rs of 𝔽q satisfying r1 + ⋯ + rs = 0, let [Formula: see text] denote the maximal cardinality of a set [Formula: see text] which contains no non-trivial solution of r1x1 + ⋯ + rsxs = 0 with xi ∈ A (1 ≤ i ≤ s). We prove that [Formula: see text].

The Erdős–Burgess constant of the multiplicative semigroup of a factor ring of 𝔽q[x]

2019 ◽  
Vol 15 (01) ◽  
pp. 131-136 ◽  
Author(s):  
Haoli Wang ◽  
Jun Hao ◽  
Lizhen Zhang
Keyword(s):  
Lower Bound ◽  
Finite Field ◽  
Prime Ideal ◽  
Polynomial Ring ◽  
Prime Power ◽  
Quotient Ring ◽  
Prime Ideals ◽  
Multiplicative Semigroup ◽  
Associative Operation ◽  
Sharp Lower Bound

Let [Formula: see text] be a commutative semigroup endowed with a binary associative operation [Formula: see text]. An element [Formula: see text] of [Formula: see text] is said to be idempotent if [Formula: see text]. The Erdős–Burgess constant of [Formula: see text] is defined as the smallest [Formula: see text] such that any sequence [Formula: see text] of terms from [Formula: see text] and of length [Formula: see text] contains a nonempty subsequence, the sum of whose terms is idempotent. Let [Formula: see text] be a prime power, and let [Formula: see text] be the polynomial ring over the finite field [Formula: see text]. Let [Formula: see text] be a quotient ring of [Formula: see text] modulo any ideal [Formula: see text]. We gave a sharp lower bound of the Erdős–Burgess constant of the multiplicative semigroup of the ring [Formula: see text], in particular, we determined the Erdős–Burgess constant in the case when [Formula: see text] is the power of a prime ideal or a product of pairwise distinct prime ideals in [Formula: see text].

Large values of Dirichlet L-functions over function fields

2020 ◽  
Vol 16 (05) ◽  
pp. 1081-1109
Author(s):  
Dragan Đokić ◽  
Nikola Lelas ◽  
Ilija Vrećica
Keyword(s):  
Lower Bound ◽  
Finite Field ◽  
Function Field ◽  
Function Fields ◽  
Resonance Method ◽  
Dirichlet Characters ◽  
Field Setting

In this paper, we investigate the existence of large values of [Formula: see text], where [Formula: see text] varies over non-principal characters associated to prime polynomials [Formula: see text] over finite field [Formula: see text], as [Formula: see text], and [Formula: see text]. When [Formula: see text], we provide a lower bound for the number of such characters. To do this, we adapt the resonance method to the function field setting. We also investigate this problem for [Formula: see text], where now [Formula: see text] varies over even, non-principal, Dirichlet characters associated to prime polynomials [Formula: see text] over [Formula: see text], as [Formula: see text]. In addition to resonance method, in this case, we use an adaptation of Gál-type sums estimate.

Regulators and class numbers of an infinite family of quintic function fields

2018 ◽  
Vol 185 (2) ◽  
pp. 107-125
Author(s):  
Jungyun Lee ◽  
Yoonjin Lee
Keyword(s):  
Function Fields ◽  
Infinite Family ◽  
Class Numbers

The Pintz–Steiger–Szemerédi estimate for intersective quadratic polynomials in function fields

2021 ◽  
pp. 1-50
Author(s):  
Guoquan Li
Keyword(s):  
Finite Field ◽  
Natural Number ◽  
Polynomial Ring ◽  
Function Fields ◽  
Difference Set ◽  
Quadratic Polynomial ◽  
Quadratic Polynomials ◽  
Number Formula ◽  
The Difference

Let [Formula: see text] be the polynomial ring over the finite field [Formula: see text] of [Formula: see text] elements. For a natural number [Formula: see text] let [Formula: see text] be the set of all polynomials in [Formula: see text] of degree less than [Formula: see text] Let [Formula: see text] be a quadratic polynomial over [Formula: see text] Suppose that [Formula: see text] is intersective, that is, which satisfies [Formula: see text] for any [Formula: see text] with [Formula: see text] where [Formula: see text] denotes the difference set of [Formula: see text] Let [Formula: see text] Suppose that [Formula: see text] and that the characteristic of [Formula: see text] is not divisible by 2. It is proved that [Formula: see text] for any [Formula: see text] where [Formula: see text] is a constant depending only on [Formula: see text] and [Formula: see text]

Multidimensional Vinogradov-type Estimates in Function Fields

2014 ◽  
Vol 66 (4) ◽  
pp. 844-873 ◽  
Author(s):  
Wentang Kuo ◽  
Yu-Ru Liu ◽  
Xiaomei Zhao
Keyword(s):  
Finite Field ◽  
Polynomial Ring ◽  
Function Fields ◽  
Circle Method ◽  
Asymptotic Formulas ◽  
Linear Spaces

AbstractLet 𝔽q[t] denote the polynomial ring over the finite field 𝔽q. We employ Wooley's new efficient congruencing method to prove certain multidimensional Vinogradov-type estimates in 𝔽q[t]. These results allow us to apply a variant of the circle method to obtain asymptotic formulas for a system connected to the problem about linear spaces lying on hypersurfaces defined over 𝔽q[t].

Prothrombin Metz : Purification and Characterization of a Variant of Human Prothrombin

1979 ◽  
Author(s):  
M Ribieto ◽  
J Elion ◽  
D Labie ◽  
F Josso
Keyword(s):  
Molecular Weight ◽  
Gel Electrophoresis ◽  
Polyacrylamide Gel Electrophoresis ◽  
Factor Xa ◽  
Polyacrylamide Gel ◽  
Cleavage Pattern ◽  
Purification And Characterization ◽  
Double Immunodiffusion ◽  
The Family

For the purification of the abnormal prothrombin (Pt Metz), advantage has been taken of the existence in the family of three siblings who, being double heterozygotes for Pt Metz and a hypoprothrombinemia, have no normal Pt. Purification procedures included barium citrate adsorption and chromatography on DEAE Sephadex as for normal Pt. As opposed to some other variants (Pt Barcelona and Madrid), Pt Metz elutes as a single symetrical peak. By SDS polyacrylamide gel electrophoresis, this material is homogeneous and appears to have the same molecular weight as normal Pt. Comigration of normal and abnormal Pt in the absence of SDS, shows a double band suggesting an abnormal charge for the variant. Pt Metz exhibits an identity reaction with the control by double immunodiffusion. Upon activation by factor Xa, Pt Metz can generate amydolytic activity on Bz-Phe-Val-Arg-pNa (S2160), but only a very low clotting activity. Clear abnormalities are observed in the cleavage pattern of Pt Metz when monitored by SDS gel electrophoresis. The main feature are the accumulation of prethrombin l (Pl) and the appearance of abnormal intermediates migrating faster than Pl.

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