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# Questions tagged [modular-forms]

Questions about modular forms and related areas

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### Questions about modular forms and the role of monodromy

Let $N \geq 3$ and let $\Gamma=\Gamma_1(N)$, so that the moduli problem for elliptic curves with $\Gamma$-structure is fine. Let $Y=Y(\Gamma)$ be the corresponding moduli space. In this context, one ...
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### Half-integral weight slash operator

I am aware that the correct way to look at modular forms of half-integral weight is on the metaplectic cover of $\mathrm{SL}_2(\mathbb R)$. Assume however that we insist on considering them as ...
0answers
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### Kronecker limit formula, modular curves, and the class number problem

Let $$Q(x,y)=ax^2+bxy+cy^2$$ be a positive definite quadratic form with $a>0$ and $D=b^2-4ac<0$. Let $$\zeta_Q(s)=\sideset{}{'}\sum_{m,n}Q(m,n)^{-s},$$ the accent indicating that $(0,0)$ is ...
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### Level Lowering Galois representations over Totally real fields

Let $F$ be a totally real number field and $\mathbb{F}$ a finite field. Let $\bar{\rho}:\text{Gal}(\bar{F}/F)\rightarrow \text{GL}_2(\mathbb{F})$ an irreducible Galois representation arising from a ...
1answer
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I asked this on mathstackexchange, but got no answer. Let $N\geq1$ be an integer, and let $\mathbb{T}$ be the Hecke algebra acting on the cusp forms of weight k and level $\Gamma_0(N)$. Then $\... 0answers 162 views ### What is definition of Cohen–Eisenstein series? I only find Cohen–Eisenstein series of weight 3/2 (in the paper A note on the Fourier coefficients of a Cohen-Eisenstein series). I founded some general definition in "Modular Forms with Integral and ... 0answers 158 views ### Diophantine applications of Paramodularity I’ve asked this question to quite a few people in person and so far haven’t seen a good answer...but I believe one should exist, so here goes! Ok, we all know how to (roughly) prove Fermat’s Last ... 0answers 41 views ### Algebraic independece of modular forms for Fricke group over$\mathbb C(q)$Let$q=e^{\pi i \tau}$for$\tau \in \mathbb H$and $$P_2(q)=\frac{P(q)+2P(q^2)}{3}, \quad Q_2(q)=\frac{Q(q)+4Q(q^2)}{5}, \\ R_2(q)=\frac{R(q)+8R(q^2)}{9},$$ a Fourier series of quasi-modular form ... 2answers 383 views ### About different cohomology theories used to study Shimura varieties The classical theory of Eichler-Shimura realizes the space of cusp forms of certain weights and levels in the parabolic cohomology of modular curves, which is the image of the cohomology with compact ... 1answer 124 views ### Characterizing a modular form via its first Fourier coefficients at infinity It is well known that a cusp form $$f = \sum_{n\ge 1}a_n q^n$$ of weight$k$and level$1$is determined by its first$d_k = \text{dim } S_k$coefficients. This follows from the valence formula (... 1answer 194 views ### Сomplement of the set of numbers of the form$ 4mn - m - n$? Numbers of the form$4mn-m-n$where$m,n\in\mathbb{Z}^+$are $$A=\{2, 5, 8, 11, 12, 14, 17, 19, 20, 23, 26, 29, 30, 32, 33, 35, \ldots\}$$ The set complement of the above set is$$B=\{1, 3, 4, 6, ... 0answers 67 views ### Maass forms associated with Ramanujan's mock theta functions If you perform a fulltext search on the L-functions and modular forms database for "Ramanujan", you get entries related to the$\tau$function and the modular discriminant$\Delta$. If you want the ... 1answer 97 views ### Complex L-functions for Hermitian modular forms? Fix an imaginary quadratic field$K$, and let$\mathcal{O}_K$be its ring of integers. A Hermitian modular form of genus 1 (i.e., an automorphic form on$GU(1,1)$) of weight$(k_1,k_2)$on a ... 0answers 141 views ### Representation of the space of lattices in$\Bbb R^n$The space of 2D lattices in$\Bbb R^2$can be represented with the two Eisenstein series$G_4$and$G_6$. Each lattice uniquely maps to a point in$\Bbb C^2$using these two invariants, and the points ... 0answers 58 views ### Is there an analogue of theta cycles for more general mod p automorphic forms? The theory of$\theta$-cycles (due to Tate, I think) and filtrations is to me a very beautiful and powerful tool in proving many statements about mod$p\$ modular forms in more explicit and elementary ...

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