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Everything about Theta function
Special functions of several complex variables
In mathematics, theta functions are special functions of several complex variables. Fundamentally, they are a family of continuous functions which encode the behavior of discrete multi-dimensional periodic systems, such as crystal lattices or points on a torus. Because they are smooth, they allow the study and manipulation of discrete combinatorial systems using the tools of analysis. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Theta functionA 5-minute orientation
- Skim a recent paper: ACSS2 acts as a lactyl-CoA synthetase and couples KAT2A to function as a lactyltransferase for histone lactylation and tumor immune evasionInfluential work since 2022
- Pick up a classic book: Kummer's quartic surfaceThe most-reprinted book on the subject
- Read the landmark paper: Hippocampal Theta: a Sensory-inhibition Theory of FunctionCited 64 times
- Go sideways: Rogers–Ramanujan continued fractionA closely related topic
- Go sideways: Jacobi elliptic functionsA closely related topic
📖 Definitions
Noun Any of a group of special functions of several complex variables, important in many areas, including the theories of abelian varieties and moduli spaces, and of quadratic forms.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Hippocampal Theta: a Sensory-inhibition Theory of Function
Riemann surfaces and the theta function
Theta-function identities and the explicit formulas for theta-function and their applications
Computational theories on the function of theta oscillations
Hardy–Petrovitch–Hutchinson’s problem and partial theta function
A theta function identity and its implications
Theta function identities
Residue Theorem and Theta Function Identities
🆕 Influential since 2022
ACSS2 acts as a lactyl-CoA synthetase and couples KAT2A to function as a lactyltransferase for histone lactylation and tumor immune evasion
Intermittent theta-burst stimulation improves motor function by inhibiting neuronal pyroptosis and regulating microglial polarization via TLR4/NFκB/NLRP3 signaling pathway in cerebral ischemic mice
New truncated theorems for three classical theta function identities
Different Music Training Modulates Theta Brain Oscillations Associated with Executive Function
On second order mock theta function $ B(q) $
📚 Books worth reading
Kummer's quartic surfaceRonald William Henry Turnbull Hudson · 1905
Compactification of Siegel moduli schemesChing-Li Chai · 1984
Die Lehre von den elliptischen integralen und den Theta-functionenKarl Heinrich Schellbach · 1864
Untersuchungen über ThetafunctionenWilhelm Wirtinger · 1895
Abel's theorem and the allied theoryHenry Frederick Baker · 1897
Neue Grundlagen einer Theorie der allgemeinen ThetafunctionenAdolf Krazer · 1892
A Brief Introduction to Theta FunctionsRichard Ernest Bellman · 1961
Lehrbuch der ThetafunktionenAdolf Krazer · 1903
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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