##
finite field

Overview page. Subjects: Computing.

A (mathematical) field with a finite number of elements. The number of elements must be of the form *p*
*
^{k}
* where

*p*is some prime number and

*k*is a...

##
finite field

in** A Dictionary of Computer Science**

January 2016; p ublished online January 2016 .

Reference Entry. Subjects: Computing. 52 words.

A (mathematical) *field with a finite number of elements. The number of elements must be of the form *p*

##
finite field

in** A Dictionary of Computing**

January 2008; p ublished online January 2008 .

Reference Entry. Subjects: Computing. 53 words.

A (mathematical) *field with a finite number of elements. The number of elements must be of the form *p*

##
finite field

Overview page. Subjects: Computing.

A (mathematical) field with a finite number of elements. The number of elements must be of the form *p*
*
^{k}
* where

*p*is some prime number and

*k*is a...

##
Proper Toric Maps Over Finite Fields

in** International Mathematics Research Notices**

January 2015; p ublished online March 2015 .

Journal Article. Subjects: Mathematics; Pure Mathematics. 6405 words.

We determine a strong form of the decomposition theorem for proper toric maps over finite fields.

##
The Situation over a Finite Field

in** Convolution and Equidistribution**

January 2012; p ublished online October 2017 .

Chapter. Subjects: Number Theory. 2195 words.

This chapter deals with the case of a finite field *k*, and a group scheme 𝓖/*k*. which is a form of 𝔾ₘ.

##
Arithmetic Correlations Over Large Finite Fields

in** International Mathematics Research Notices**

January 2016; p ublished online June 2015 .

Journal Article. Subjects: Mathematics; Pure Mathematics. 3174 words.

The auto-correlations of arithmetic functions, such as the von Mangoldt function, the M[math] bius function, and the divisor function, are the subject of classical problems in analytic...

##
VALUE SETS OF POLYNOMIAL MAPS OVER FINITE FIELDS

in** The Quarterly Journal of Mathematics**

December 2013; p ublished online October 2012 .

Journal Article. Subjects: Pure Mathematics. 0 words.

We provide upper bounds for the cardinality of the value set of a polynomial map in several variables over a finite field. These bounds generalize earlier bounds for univariate polynomials.

null...##
Quantum Field Theory At Finite Temperature: Equilibrium Properties

in** Quantum Field Theory and Critical Phenomena**

June 2002; p ublished online January 2010 .

Chapter. Subjects: Mathematical and Statistical Physics. 14589 words.

This chapter reviews some equilibrium properties in Statistical Quantum Field Theory, that is, relativistic Quantum Field Theory (QFT) at finite temperature, a relativistic extension of the...

##
Curves in abelian varieties over finite fields

in** International Mathematics Research Notices**

January 2005; p ublished online January 2005 .

Journal Article. Subjects: Mathematics. 0 words.

Over an algebraic closure of a finite field, we show that multiples of a curve generating an abelian variety cover the whole abelian variety. As a corollary, there exist varieties over such...

##
Group Structures of Elliptic Curves Over Finite Fields

in** International Mathematics Research Notices**

January 2014; p ublished online June 2013 .

Journal Article. Subjects: Mathematics. 3135 words.

It is well known that if *E* is an elliptic curve over the finite field , then for some positive integers *m*,*k*. Let *S*(*M*,*K*) denote the set of pairs (*m*,*k*) with *m*≤*M* and *k*≤*K* for which there...

##
Sum-product Estimates in Finite Fields via Kloosterman Sums

in** International Mathematics Research Notices**

January 2007; p ublished online January 2007 .

Journal Article. Subjects: Mathematics; Pure Mathematics. 0 words.

We establish improved sum-product bounds in finite fields using incidence theorems based on bounds for classical Kloosterman and related sums.

##
Relativistic Mean-Field Theory with the Pion in Finite Nuclei

in** Progress of Theoretical Physics**

November 2002; p ublished online November 2002 .

Journal Article. 0 words.

We study the possibility of the existence of a finite pion mean field in finite nuclei in the relativistic mean-field (RMF) theory. We are led to conjecture this existence by findings of...

##
Chiral Sigma Model with Pion Mean Field in Finite Nuclei

in** Progress of Theoretical Physics**

January 2004; p ublished online January 2004 .

Journal Article. 0 words.

The properties of infinite matter and finite nuclei are studied using the chiral sigma model in the framework of relativistic mean field theory. We reconstruct an extended chiral sigma...

##
Hardy–Littlewood Tuple Conjecture Over Large Finite Fields

in** International Mathematics Research Notices**

January 2014; p ublished online November 2012 .

Journal Article. Subjects: Mathematics. 1614 words.

We prove the following function field analog of the Hardy–Littlewood conjecture (which generalizes the twin prime conjecture) over large finite fields. Let *n* and *r* be positive integers and *q*null...

##
Relative Motives and the Theory of Pseudo-finite Fields

in** International Mathematics Research Papers**

January 2007; p ublished online January 2007 .

Journal Article. Subjects: Mathematics. 0 words.

We generalize the motivic incarnation morphism from the theory of arithmetic integration to the relative case, where we work over a base variety *S* over a field *k* of characteristic zero. We...

##
POLYNOMIAL VALUES IN SUBFIELDS AND AFFINE SUBSPACES OF FINITE FIELDS

in** The Quarterly Journal of Mathematics**

June 2015; p ublished online December 2014 .

Journal Article. Subjects: Pure Mathematics. 4859 words.

For an integer [math], a prime power [math] and a polynomial [math] over a finite field [math] of [math] elements, we obtain an upper bound on the frequency of elements in an orbit...

##
Gindikin–Karpelevich Finiteness for Kac–Moody Groups Over Local Fields

in** International Mathematics Research Notices**

November 2017; p ublished online October 2016 .

Journal Article. Subjects: Mathematics; Pure Mathematics. 7349 words.

**Abstract**

In this article, we prove some finiteness results about split Kac–Moody groups over local non-archimedean fields. Our results generalize those of “An...

##
An analog of Tate's conjecture over local and finitely generated fields

in** International Mathematics Research Notices**

January 2000; p ublished online January 2000 .

Journal Article. Subjects: Mathematics. 0 words.

Let *K* be a local non-Archimedean field, *p* the characteristic of the residue field of *K*,*l* a prime number different from the characteristic of *K*,*X* a separated scheme of finite type over...

##
Frobenius distributions of elliptic curves over finite prime fields

in** International Mathematics Research Notices**

January 2003; p ublished online January 2003 .

Journal Article. Subjects: Mathematics. 0 words.

We study the number *H*(*t,p*) of isomorphism classes of elliptic curves with Frobenius trace *t* ∈ ℤ over the finite field F*
_{p}
*. It may be predicted through a...

##
DIVISIBILITY OF EXPONENTIAL SUMS AND SOLVABILITY OF CERTAIN EQUATIONS OVER FINITE FIELDS

in** The Quarterly Journal of Mathematics**

June 2009; p ublished online June 2008 .

Journal Article. Subjects: Pure Mathematics. 0 words.

Carlitz [Solvability of certain equations in a finite field, *Quart. J. Math.* (*Oxford*) 7 (1956), 3–4] determined conditions under which infinite families of polynomials have solutions in a...