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Mock modular form: History, Applications & Art

In mathematics, a mock modular form is the holomorphic part of a harmonic weak Maass form, and a mock theta function is essentially a mock modular form of weight ⁠1/2⁠. The first examples of mock theta functions were described by Srinivasa Ramanujan in his last 1920 letter to G. H. Hardy and in his lost notebook. Sander Zwegers discovered that adding…

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Mock modular form topic overview

The analysis highlights History, Applications and Art as prominent areas in the source structure around Mock modular form.

Related topics
49
Source areas
7
Connected nodes
56
Extracted relationships
29
Concept neighborhoods
29
Bridge connections
56

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.

History · 16 topics
Definition · 10 topics
Overview · 7 topics
Applications · 6 topics
Examples · 6 topics
Appell–Lerch sums · 3 topics
Indefinite theta series · 1 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

Less obvious directions

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

History

Definition

Appell–Lerch sums

Indefinite theta series

Applications

Examples

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 Mock modular form connects Entity context

The extracted context around Mock modular form shows recurring relationship patterns in the source. For example, Mock modular form → Atish Dabholkar, Don Zagier, Lie, Mock, Ruth Lawrence, Sameer Murthy, Semikhatov, Taormina, Troost, Yu Tipunin Another extracted example is Mock modular form → Appell, Lambert, Lerch, Mathias Lerch, Paul, The Appell, Watson, Zwegers. Use these groups to spot repeated connection types before inspecting the individual relationships.

Mock modular form

Top relations

has application · 10
Mock modular form → Atish Dabholkar, Don Zagier, Lie, Mock, Ruth Lawrence, Sameer Murthy, Semikhatov, Taormina, Troost, Yu Tipunin
related to Appell–Lerch sums · 8
Mock modular form → Appell, Lambert, Lerch, Mathias Lerch, Paul, The Appell, Watson, Zwegers
related to Examples · 7
Mock modular form → Any, Don Zagier, Eisenstein, Fourier, Hurwitz, Maass, The
related to Definition · 3
Mock modular form → Fix, Maass, SL2
is a · 1
Mock modular form → holomorphic part of a harmonic weak Maass form

Important terminology

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

Important terminology

mock theta functions modular forms weight function form maass weak holomorphic ramanujan order zwegers harmonic found cusps series group lerch

Mock modular form relationships Subject–Predicate–Object triples

TTTA extracted 29 structured relationships around Mock modular form. Examples in this analysis include Mock modular form → is a → holomorphic part of a harmonic weak Maass form and Mock modular form → has application → Ruth Lawrence. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Mock modular formis aholomorphic part of a harmonic weak Maass form0.90text
Mock modular formhas applicationRuth Lawrence0.60section
Mock modular formhas applicationDon Zagier0.60section
Mock modular formhas applicationSemikhatov0.60section
Mock modular formhas applicationTaormina0.60section
Mock modular formhas applicationYu Tipunin0.60section
Mock modular formhas applicationLie0.60section
Mock modular formhas applicationTroost0.60section
Mock modular formhas applicationMock0.60section
Mock modular formhas applicationAtish Dabholkar0.60section
Mock modular formhas applicationSameer Murthy0.60section
Mock modular formrelated to Appell–Lerch sumsAppell0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Mock modular form bring nearby vocabulary together. In this analysis, examples include Theta, Functions and Modular. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Mock modular form
    • Theta
    • Functions
    • Modular
    • Forms
    • Weight
    • Order
    • Form
    • Mock
    • Ramanujan
    • Function
    • Maass
    • Series
  • mock modular form
    • Theta
    • Functions
    • Forms
    • Weight
    • Modular
    • Weak
    • Maass
    • Function
    • Shadow
    • Harmonic
    • Order
    • Cusps
  • holomorphic
    • Harmonic
    • Maass
    • Weight
    • Weak
    • Modular
    • Function
    • Forms
    • Mock
    • Showed
    • Cusps
    • Theta
    • Order
  • maass form
    • Weak
    • Weight
    • Modular
    • Maass
    • Function
    • Forms
    • Shadow
    • Harmonic
    • Zwegers
    • Holomorphic
    • Mock
    • Cusps
  • srinivasa ramanujan
    • Lost
    • Notebook
    • Found
    • Proved
    • Order
    • Theta
    • Group
    • Andrews
    • Identities
    • Watson
    • Given
    • Ramanujan's
  • sander zwegers
    • Maass
    • Forms
    • Theta
    • Weak
    • Functions
    • Indefinite
    • Sums
    • Lerch
    • Mock
    • Harmonic
    • Watson
    • Meromorphic
  • asymptotic expansions
    • Studied
    • Examples
    • Andrews
    • Cusps
    • Series
    • Function
    • Forms
    • Order
    • Weight
    • Called
    • Form
    • Indefinite
  • theta functions
    • Functions
    • Theta
    • Mock
    • Forms
    • Order
    • Ramanujan
    • Weight
    • Modular
    • Zwegers
    • Found
    • Terms
    • Andrews

Connections between topic areas Semantic bridges

For Mock modular form, one of the stronger structural bridges in this analysis connects Mock modular form with History. 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
Mock modular form — History · splits 40 ⟂ 17
Mock modular form — Definition · splits 46 ⟂ 11
Mock modular form — Overview · splits 49 ⟂ 8
Mock modular form — Applications · splits 50 ⟂ 7
Mock modular form — Examples · splits 50 ⟂ 7
Mock modular form — Appell–Lerch sums · splits 53 ⟂ 4

Map overview Semantic statistics

Mock modular form

Nodes57
Edges56
Triples29
Avg. degree1.96
Density0.035088
Components1

Source & methodology

TTTA analyzes the structure around Mock modular form to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as History, Applications & Art, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Mock modular form · EN edition · Analysis: TopicsToTalkAbout

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