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Kummer sum: Statistical questions, Definition & Cassels' conjecture

In mathematics, Kummer sum is the name given to certain cubic Gauss sums for a prime modulus p, with p congruent to 1 modulo 3. They are named after Ernst Kummer, who made a conjecture about the statistical properties of their arguments, as complex numbers. These sums were known and used before Kummer, in the theory of cyclotomy.

Language: English [EN]
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Kummer sum topic overview

The analysis highlights Statistical questions, Definition and Cassels' conjecture as prominent areas in the source structure around Kummer sum.

Related topics
28
Source areas
5
Connected nodes
33
Extracted relationships
11
Concept neighborhoods
17
Bridge connections
33

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Statistical questions · 16 topics
Overview · 4 topics
Cassels' conjecture · 3 topics
Definition · 3 topics
Patterson's conjecture · 2 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Suggested research paths

A focused starting point derived from the topic graph, ranked independently of the source article order.

Start with these areas

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Definition

Statistical questions

Cassels' conjecture

Patterson's conjecture

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Kummer sum connects Entity context

The extracted context around Kummer sum shows recurring relationship patterns in the source. For example, Kummer sum → Cassels, Charles Matthews, Eisenstein, Kummer, The, This, Tomio Kubota Another extracted example is Kummer sum → Dirichlet, Given, Kummer. Use these groups to spot repeated connection types before inspecting the individual relationships.

Kummer sum

Top relations

related to Cassels' conjecture · 7
Kummer sum → Cassels, Charles Matthews, Eisenstein, Kummer, The, This, Tomio Kubota
related to Definition · 3
Kummer sum → Dirichlet, Given, Kummer
is a · 1
Kummer sum → name given to certain cubic Gauss sums for a prime modulus p

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

kummer sums conjecture sum gauss fact cubic made theory statistical work heath-brown prime modulo known argument mathematics cube exponential form

Kummer sum relationships Subject–Predicate–Object triples

TTTA extracted 11 structured relationships around Kummer sum. Examples in this analysis include Kummer sum → is a → name given to certain cubic Gauss sums for a prime modulus p and Kummer sum → related to Cassels' conjecture → Kummer. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Kummer sumis aname given to certain cubic Gauss sums for a prime modulus p0.90text
Kummer sumrelated to Cassels' conjectureKummer0.60section
Kummer sumrelated to Cassels' conjectureCassels0.60section
Kummer sumrelated to Cassels' conjectureTomio Kubota0.60section
Kummer sumrelated to Cassels' conjectureThis0.60section
Kummer sumrelated to Cassels' conjectureEisenstein0.60section
Kummer sumrelated to Cassels' conjectureThe0.60section
Kummer sumrelated to Cassels' conjectureCharles Matthews0.60section
Kummer sumrelated to DefinitionKummer0.60section
Kummer sumrelated to DefinitionDirichlet0.60section
Kummer sumrelated to DefinitionGiven0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Kummer sum bring nearby vocabulary together. In this analysis, examples include Sums, Conjecture and Cube. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Kummer sum
    • Sums
    • Conjecture
    • Cube
    • Sum
    • Exponential
    • Modulo
    • Statistical
    • Cubic
    • Made
    • Mathematics
    • Numbers
    • Used
  • kummer sum
    • Modulo
    • Sums
    • Conjecture
    • Argument
    • Cube
    • Exponential
    • Prime
    • Statistical
    • Sum
    • Cubic
    • Made
    • Mathematics
  • gauss sums
    • Prime
    • Sums
    • Sum
    • Cube
    • Known
    • Linear
    • Exponential
    • Fact
    • Theory
    • Given
    • Mathematics
    • Multiplication
  • ernst kummer
    • Sums
    • Conjecture
    • Sum
    • Exponential
    • Modulo
    • Statistical
    • Cubic
    • Made
    • Mathematics
    • Numbers
    • Used
    • Argument
  • cassels' conjecture
    • Statistical
    • Made
    • Kummer
    • Kummer's
    • Modulo
    • Heath-brown
    • Sum
    • Character
    • Complex
    • Numbers
    • Properties
    • Roots
  • patterson's conjecture
    • Statistical
    • Made
    • Kummer
    • Kummer's
    • Modulo
    • Heath-brown
    • Sum
    • Character
    • Complex
    • Numbers
    • Properties
    • Roots
  • cube roots of unity
    • Roots
    • Unity
    • Cube
    • Character
    • Linear
    • Multiplication
    • One
    • Gauss
    • Sum
    • Exponential
    • Modulo
    • Statistical
  • cubic residue symbol
    • Exponential
    • Sums
    • Sum
    • Kummer
    • Given
    • Linear
    • Mathematics
    • One
    • Two
    • Modulo
    • Prime
    • Fact

Connections between topic areas Semantic bridges

For Kummer sum, one of the stronger structural bridges in this analysis connects Kummer sum with Statistical questions. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Kummer sum — Statistical questions · splits 17 ⟂ 17
Kummer sum — Overview · splits 29 ⟂ 5
Kummer sum — Definition · splits 30 ⟂ 4
Kummer sum — Cassels' conjecture · splits 30 ⟂ 4
Kummer sum — Patterson's conjecture · splits 31 ⟂ 3

Map overview Semantic statistics

Kummer sum

Nodes34
Edges33
Triples11
Avg. degree1.94
Density0.058824
Components1

Source & methodology

TTTA analyzes the structure around Kummer sum to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Statistical questions, Definition & Cassels' conjecture, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Kummer sum · EN edition · Analysis: TopicsToTalkAbout

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