<em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

    <em id="zlul0"></em>

      <dl id="zlul0"></dl>
        <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
        <em id="zlul0"></em>

        <div id="zlul0"><ol id="zlul0"></ol></div>

        Stack Exchange Network

        Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

        Visit Stack Exchange

        Questions tagged [modular-forms]

        Questions about modular forms and related areas

        0
        votes
        0answers
        21 views

        Coset representatives of a principal congruence subgroup by another principal congruence subgroup

        Consider the principal congruence subgroup $\Gamma(N)$, this consists of entries in $\mathrm{SL}_2(\mathbb{Z})$ congruent to the identity modulo $N$. Consider another principal congruence subgroup $\...
        6
        votes
        1answer
        536 views

        Galois theory of modular functions

        Let $\mathcal M_m$ be the set of $2$-by-$2$ primitive (relatively prime entries) matrices with determinant $m$. Let $\alpha \in \mathcal M_m$ and let $\Gamma\subset \operatorname{SL}_2(\mathbb Z)$. ...
        2
        votes
        0answers
        97 views

        Newman's conjecture of Partition function

        (Sorry for my poor english....) Let $p(n)$ be a partition function and $M$ be an integer. Newman conjectured that for each $0\leq r\leq M-1$, there are infinitely many integers $n$ such that \begin{...
        3
        votes
        1answer
        191 views

        Why are Poincare series defined as they are?

        We know the Poincare series are defined as the following: The $m^{th}$ Poincare series of weight $k$ for $\Gamma$ is: $$ P_{m}^{k} (z) = \sum_{(c,d)=1} (cz+d)^{-k} e^{2 \pi in(\tau z)}. $$ The ...
        1
        vote
        0answers
        66 views

        theta function with a low bound in the sum

        I encounter a sum similar to the Jacobi Theta function except there is a lower bound $-J$ with $J\geq 0$: \begin{equation} f(q,x)=\sum_{n=-J}^\infty q^{n^2}x^n. \end{equation} My question is whether ...
        2
        votes
        0answers
        87 views

        How to express the cuspidal form in terms of Poincare series?

        Sorry to disturb. I recently read Blomer's paper. There is a blur which needs the expert's help here. Blomer's paper says "For any cusp form $f$ of integral weight $k$, level $N$, $f$ can be written ...
        3
        votes
        0answers
        109 views

        Is constant map from automorphic form surjective?

        Let $G$ be a connected reductive group over $\mathbb{Q}$ and $P=NM$ be a standard parabolic subgroup of $G$ and and $K$ a 'good' maximal compact subgroup of $G$. (For precise definitions of these ...
        3
        votes
        0answers
        97 views

        Automorphy Factor from Vector Bundles on Compact Dual

        So I'm coming from an algebraic geometry perspective and I'm trying to carefully piece together the story of interpreting automorphic forms as sections of vector bundles on Shimura varieties. I think ...
        6
        votes
        0answers
        136 views

        Additive and multiplicative convolution deeply related in modular forms

        From the fact spaces of modular forms are finite dimensional, from the decomposition in Hecke eigenforms, and from the duplication formula for $\Gamma(s)$ there are a lot of identities mixing additive ...
        2
        votes
        0answers
        81 views

        Deforming Modular Symbols

        This is probably a silly question, as I don't really know a whole lot about modular symbols over arbitrary rings. How do modular symbols over a finite field square with Katz modular forms? If they ...
        6
        votes
        2answers
        334 views

        Are these 5 the only eta quotients that parameterize $x^2+y^2 = 1$?

        Given the Dedekind eta function $\eta(\tau)$, define, $$\alpha(\tau) =\frac{\sqrt2\,\eta(\tau)\,\eta^2(4\tau)}{\eta^3(2\tau)}$$ $$\beta(\tau) =\frac{\eta^2(\tau)\,\eta(4\tau)}{\eta^3(2\tau)}\quad\;$$...
        1
        vote
        0answers
        99 views

        “Modularity” of generalized theta series

        The most basic theta series is defined by $\theta(z)=\sum_{n=-\infty}^{\infty}q^{n^2}$, where $q=e^{2\pi iz}$. This is connected to the question of how many representatations does an integer $n$ have ...
        4
        votes
        0answers
        189 views

        What role do Hecke operators and ideal classes perform in “Quantum Money from Modular Forms?”

        Cross-posted on QCSE An interesting application of the no-cloning theorem of quantum mechanics/quantum computing is embodied in so-called quantum money - qubits in theoretically unforgeable states. ...
        1
        vote
        0answers
        82 views

        Igusa curve at infinite level

        In the paper "Le halo spectral" (http://perso.ens-lyon.fr/vincent.pilloni/halofinal.pdf) and in the following paper "The adic cuspidal, Hilbert eigenvarieties" (http://perso.ens-lyon.fr/vincent....
        5
        votes
        1answer
        115 views

        Asymptotic's for Fourier coefficients of $GL(3)$ Maass forms

        Let $f$ be a $GL(3)$ Hecke-Maass cusp form and $A(m,n)$ denote its Fourier coefficients. Are there any lower bounds known for $\sum_{p\leq x}|A(1,p)|^2$ or $\sum_{n\leq x}|A(1,n)|^2$ ? (we know the ...

        15 30 50 per page
        山西福彩快乐十分钟
          <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

          <em id="zlul0"></em>

            <dl id="zlul0"></dl>
              <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
              <em id="zlul0"></em>

              <div id="zlul0"><ol id="zlul0"></ol></div>
                <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

                <em id="zlul0"></em>

                  <dl id="zlul0"></dl>
                    <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
                    <em id="zlul0"></em>

                    <div id="zlul0"><ol id="zlul0"></ol></div>