All Questions
Tagged with eisenstein-series modular-forms
13 questions with no upvoted or accepted answers
11
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0
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231
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Eisenstein series for non congruence subgoups
What is the present status of the Eisenstein series for noncongruence subgroups?
I am aware of work of A. Scholl and Rohrlich work on the subject.
Is there any specific examples that has been ...
- 248
10
votes
0
answers
152
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Is there some precise way in which modular cocycle $c/(c\tau +d)$ "is" the generator of $H^1(\mathcal{M}_{ell}, \omega^2) \cong \mathbb{Z}/12$?
It is semiclassical that the extension class $\text{Ext}^1(\omega^{-1},\omega)\cong H^1(\mathcal{M}_{ell},\omega^2)$ over the modular stack $\mathcal{M}_{ell}/\mathbb{Z}$ is nonvanishing, being cyclic ...
- 2,054
7
votes
0
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422
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Moduli interpretation of Eisenstein series
Let $N \geq 11$ be an integer and consider the basis of Eisenstein series for $M_2(\Gamma_0(N))$ described in Theorem $4.6.2$ of Diamond--Shurman's book. Pick and Eisenstein series $F$ in this basis. ...
- 1,109
6
votes
0
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176
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Factorizing classical Eisenstein series
In the course of my research, I found some surprising (for me) factorizations
of Eisenstein series in levels $1$, $2$, $3$, and $4$. For instance, in level $1$
set with standard modular form notation
$...
- 13.1k
6
votes
0
answers
467
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Eisenstein series of Hilbert modular forms
I am reading Shimura's paper "The Special Values of the Zeta Functions Associated With Hilbert Modular Forms" and I do not exactly understand his definition of the Eisenstein series in section 3.
...
- 123
4
votes
0
answers
124
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A coefficient in Dirichlet series associated with a cofinite subgroup of $\mathrm{SL}(2,\mathbb R)$
Let $\Gamma$ be a discrete subgroup of $\operatorname{SL}(2,\mathbb R)$, acting on the upper half-plane $\mathbb H$. Suppose that $\Gamma\backslash \mathbb H$ is non-compact and its compactification $\...
- 7,193
4
votes
0
answers
612
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Eisenstein series of weight one
Let $\psi$ be an odd Dirichlet character of $G_{\mathbb{Q}}$ with conductor equal to $N$ and $p \nmid N$ be a prime number. Assume that $\psi(Frob_p)=1$.
Denote by $E_{\psi,1} \in S_1(\Gamma_1(N))$ ...
- 1,066
4
votes
0
answers
164
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Counting cosets of matrices of determinant > 1 under the action of a congruence subgroup
I tried asking this on math exchange, but no luck, so thought I'd try here.
Let $M_2(m,\mathbb{Z}) $ be the $2\times 2$ matrices with integer entries and determinant $m$. Let $\Gamma^0(N)$ be the ...
- 41
3
votes
0
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441
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On nonholomorphic Eisenstein series
Could you suggest me a reference where the following non-holomorphic generalization of the Eisenstein series is discussed?
$$ G_{k,l}(\tau,z) = \sum_{m,n} (z+m+n\tau)^{-k}(\bar z+m+n\bar \tau)^{-l}
$...
- 6,133
2
votes
0
answers
98
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Extrema of real analytic Eisenstein series and more general modular functions
The real analytic Eisenstein series defined by the Poincare sum
$$E(s,z)=\sum_{(m,n)\neq (0,0)} {y^s\over |mz+n|^{2s}}$$
for $z\in{\mathbb H}$ and ${\rm Re}(s)>1$ is a manifestly $SL(2,{\mathbb Z})$...
- 21
2
votes
0
answers
304
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Question about the Fourier expansion of adelic Eisenstein series for $\operatorname{GL}_2$
My reference is Daniel Bump's book, Automorphic Forms and Representations, Chapter 3.7. Let $k$ be a number field, $G = \operatorname{GL}_2$, $B$ and $T$ the usual Borel subgroup and maximal torus ...
- 6,180
1
vote
0
answers
101
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Decomposing functions on the fundamental domain of the torus into cusp forms, eisenstein series
I am trying to do some elementary calculations to understand the properties of the following spectral resolution on $H/SL(2,\mathbf{Z})$. (Half plane mod modular group; fundamental domain of the torus)...
- 242
1
vote
0
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355
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What is definition of Cohen–Eisenstein series?
I only find Cohen–Eisenstein series of weight 3/2 (in the paper A note on the Fourier coefficients of a Cohen-Eisenstein series). I founded some general definition in "Modular Forms with Integral and ...
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