This article is about holomorphic Eisenstein series in dimension 3. For the non-holomorphic case, see Real analytic Eisenstein series. For the higher dimensional case, see Siegel Eisenstein series.
Eisenstein series, named after German mathematician Gotthold Eisenstein,[1] are particular modular forms with infinite series expansions that may be written down directly. Originally defined for the modular group, Eisenstein series can be generalized in the theory of automorphic forms.
^"Gotthold Eisenstein - Biography". Maths History. Retrieved 2023-09-05.
Eisensteinseries, named after German mathematician Gotthold Eisenstein, are particular modular forms with infinite series expansions that may be written...
In mathematics, the Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are the...
Sergei Mikhailovich Eisenstein (22 January [O.S. 10 January] 1898 – 11 February 1948) was a Soviet film director, screenwriter, film editor and film theorist...
and degree r<g, given by a series similar to an Eisensteinseries. It is a generalization of the Siegel Eisensteinseries, which is the special case when...
(2n+1)=0} . The same trick can be used to establish the sum of the Eisensteinseries: π cot ( π z ) = lim N → ∞ ∑ n = − N N ( z − n ) − 1 . {\displaystyle...
mathematics, a Siegel Eisensteinseries (sometimes just called an Eisensteinseries or a Siegel series) is a generalization of Eisensteinseries to Siegel modular...
In mathematics, the simplest real analytic Eisensteinseries is a special function of two variables. It is used in the representation theory of SL(2,R)...
annihilate the Eisensteinseries. It was introduced by Barry Mazur (1977), in studying the rational points of modular curves. An Eisenstein prime is a prime...
\Lambda (s,f)=(-1)^{\varepsilon }\Lambda (1-s,f).} The non-holomorphic Eisenstein-series is defined for z = x + i y ∈ H {\displaystyle z=x+iy\in \mathbb {H}...
terms of Eisensteinseries, and meromorphicity as well as a weak functional equation were a consequence of functional equations for Eisensteinseries. This...
identities, including relationships on the Riemann zeta function and the Eisensteinseries of modular forms. Divisor functions were studied by Ramanujan, who...
Eisenstein integral is an integral introduced by Harish-Chandra in the representation theory of semisimple Lie groups, analogous to Eisensteinseries...
75\end{aligned}}} where the reason for the squares is due to certain Eisensteinseries. For Heegner numbers d < 19 {\displaystyle d<19} , one does not obtain...
archived from the original (PDF) on 2009-03-27 Zagier, Don (1981), "Eisensteinseries and the Riemann zeta function", Automorphic forms, representation...
744=24\times 31} and the reason for the squares is due to certain Eisensteinseries. The constant e π 163 {\displaystyle e^{\pi {\sqrt {163}}}} is sometimes...
limit formula describes the constant term at s = 1 of a real analytic Eisensteinseries (or Epstein zeta function) in terms of the Dedekind eta function....
to obtain, though some have directly analytical properties: - The Eisensteinseries (which is a prototypical modular form) over certain field extensions...
is harder, because there is a continuous spectrum, described using Eisensteinseries. Selberg worked out the non-compact case when G is the group SL(2...
most 4 was 464 pages long. 1976 Eisensteinseries. Langlands's proof of the functional equation for Eisensteinseries was 337 pages long. 1983 Trichotomy...
Phyllis Eisenstein (February 26, 1946 – December 7, 2020) was an American author of science fiction and fantasy short stories as well as novels. Her work...
constructing Siegel modular forms include: Eisensteinseries Theta functions of lattices and Siegel theta series Saito–Kurokawa lift for degree 2 Ikeda lift...
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