modular form (Q1994): Difference between revisions

@@ Property / topic's main category @@
+Category:Modular forms
@@ Property / topic's main category: Category:Modular forms / rank @@
+Normal rank
@@ Property / Freebase ID @@
+/m/01q038
@@ Property / Freebase ID: /m/01q038 / rank @@
+Normal rank
@@ Property / Freebase ID: /m/01q038 / reference @@
+stated in: Freebase Data Dumps
publication date: 28 October 2013Timestamp +2013-10-28T00:00:00Z
Timezone +00:00
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++2013-10-28T00:00:00Z
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++00:00
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+Gregorian
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+day
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@@ Property / subclass of @@
+holomorphic function
@@ Property / subclass of: holomorphic function / rank @@
+Normal rank
@@ Property / subclass of @@
+meromorphic function
@@ Property / subclass of: meromorphic function / rank @@
+Normal rank
@@ Property / Library of Congress authority ID @@
+sh85050826
@@ Property / Library of Congress authority ID: sh85050826 / rank @@
+Normal rank
@@ Property / Library of Congress authority ID: sh85050826 / reference @@
+reference URL: https://github.com/JohnMarkOckerbloom/ftl/blob/master/data/wikimap
retrieved: 3 April 2019Timestamp +2019-04-03T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
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-Timestamp
++2019-04-03T00:00:00Z
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++00:00
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+Gregorian
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@@ Property / Microsoft Academic ID @@
+75764964
@@ Property / Microsoft Academic ID: 75764964 / rank @@
+Normal rank
@@ Property / nLab ID @@
+modular form
@@ Property / nLab ID: modular form / rank @@
+Normal rank
@@ Property / defining formula @@
+ ${\begin{aligned}&f\colon \mathbb {H} \to \mathbb {C} \\&\Gamma \leq \operatorname {SL} (2;\mathbb {Z} )\\&k\in \mathbb {Z} \\&\forall \gamma ={\begin{pmatrix}a&b\\c&d\end{pmatrix}}\in \Gamma \colon f(\gamma (z))=(cz+d)^{k}f(z)\\&\forall \gamma ={\begin{pmatrix}a&b\\c&d\end{pmatrix}}\in \operatorname {SL} (2;\mathbb {Z} )\colon \sup _{z\to \infty \mathrm {i} }|(cz+d)^{-k}f(\gamma (z))|<\infty \end{aligned}}$ 
\begin{aligned}&f\colon\mathbb H\to\mathbb C\\&\Gamma\le\operatorname{SL}(2;\mathbb Z)\\&k\in\mathbb Z\\&\forall\gamma=\begin{pmatrix}a&b\\c&d\end{pmatrix}\in\Gamma\colon f(\gamma(z))=(cz+d)^kf(z)\\&\forall\gamma=\begin{pmatrix}a&b\\c&d\end{pmatrix}\in\operatorname{SL}(2;\mathbb Z)\colon\sup_{z\to\infty\mathrm i}|(cz+d)^{-k}f(\gamma(z))|<\infty\end{aligned}
+Normal rank
@@ Property / National Library of Israel J9U ID @@
+987007545854805171
@@ Property / National Library of Israel J9U ID: 987007545854805171 / rank @@
+Normal rank
@@ Property / National Library of Israel J9U ID: 987007545854805171 / reference @@
+stated in: National Library of Israel
@@ Property / OpenAlex ID @@
+C75764964
@@ Property / OpenAlex ID: C75764964 / rank @@
+Normal rank
@@ Property / OpenAlex ID: C75764964 / reference @@
+stated in: OpenAlex
retrieved: 26 January 2022Timestamp +2022-01-26T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
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After 0
reference URL: https://docs.openalex.org/download-snapshot/snapshot-data-format
-Timestamp
++2022-01-26T00:00:00Z
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++00:00
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+Gregorian
-Precision
+day
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@@ Property / described by source @@
+Great Soviet Encyclopedia (1926–1947)
@@ Property / described by source: Great Soviet Encyclopedia (1926–1947) / rank @@
+Normal rank
@@ Property / Stack Exchange tag @@
+https://mathoverflow.net/tags/modular-forms
+Normal rank
@@ Property / Stack Exchange tag @@
+https://math.stackexchange.com/tags/modular-forms
+Normal rank
@@ Property / in defining formula @@
+ $f$ 
f
@@ Property / in defining formula: $f$ / rank @@
+Normal rank
@@ Property / in defining formula: $f$ / qualifier @@
+symbol represents: modular form
@@ Property / in defining formula @@
+ $\mathbb {H}$ 
\mathbb H
@@ Property / in defining formula: $\mathbb {H}$ / rank @@
+Normal rank
@@ Property / in defining formula: $\mathbb {H}$ / qualifier @@
+symbol represents: upper half-plane
@@ Property / in defining formula @@
+ $\mathbb {C}$ 
\mathbb C
@@ Property / in defining formula: $\mathbb {C}$ / rank @@
+Normal rank
@@ Property / in defining formula: $\mathbb {C}$ / qualifier @@
+symbol represents: set of complex numbers
@@ Property / in defining formula @@
+ $\operatorname {SL} (2;\mathbb {Z} )$ 
\operatorname{SL}(2;\mathbb Z)
@@ Property / in defining formula: $\operatorname {SL} (2;\mathbb {Z} )$ / rank @@
+Normal rank
+symbol represents: modular group
@@ Property / in defining formula @@
+ $\Gamma$ 
\Gamma
@@ Property / in defining formula: $\Gamma$ / rank @@
+Normal rank
@@ Property / in defining formula: $\Gamma$ / qualifier @@
+symbol represents: congruence subgroup
@@ Property / in defining formula @@
+ $\gamma$ 
\gamma
@@ Property / in defining formula: $\gamma$ / rank @@
+Normal rank
@@ Property / in defining formula: $\gamma$ / qualifier @@
+symbol represents: integer matrix
@@ Property / in defining formula @@
+ $k$ 
k
@@ Property / in defining formula: $k$ / rank @@
+Normal rank
@@ Property / in defining formula: $k$ / qualifier @@
+symbol represents: integer
@@ Property / in defining formula @@
+ $\mathbb {Z}$ 
\mathbb Z
@@ Property / in defining formula: $\mathbb {Z}$ / rank @@
+Normal rank
@@ Property / in defining formula: $\mathbb {Z}$ / qualifier @@
+symbol represents: set of integers
@@ Property / image @@
+Discriminant real part.jpeg
@@ Property / image: Discriminant real part.jpeg / rank @@
+Normal rank
@@ Property / image: Discriminant real part.jpeg / qualifier @@
+media legend: the real part of the modular discriminant, a modular form of weight 12, as a function of the nome on the unit disc (English)
@@ Property / MathWorld ID @@
+ModularForm
@@ Property / MathWorld ID: ModularForm / rank @@
+Normal rank