Modular classes of Q-manifolds: a review and some applications

Andrew James Bruce

Displaying similar documents to “Modular classes of Q-manifolds: a review and some applications”

Modular Classes of Q-Manifolds, Part II: Riemannian Structures $&$ Odd Killing Vectors Fields

Andrew James Bruce (2020)

Archivum Mathematicum

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We define and make an initial study of (even) Riemannian supermanifolds equipped with a homological vector field that is also a Killing vector field. We refer to such supermanifolds as Riemannian Q-manifolds. We show that such Q-manifolds are unimodular, i.e., come equipped with a Q-invariant Berezin volume.

The second moment of quadratic twists of modular L-functions

K. Soundararajan, Matthew P. Young (2010)

Journal of the European Mathematical Society

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We study the second moment of the central values of quadratic twists of a modular $L$ -function. Unconditionally, we obtain a lower bound which matches the conjectured asymptotic formula, while on GRH we prove the asymptotic formula itself.

The ℤ₂-cohomology cup-length of real flag manifolds

Július Korbaš, Juraj Lörinc (2003)

Fundamenta Mathematicae

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Using fiberings, we determine the cup-length and the Lyusternik-Shnirel’man category for some infinite families of real flag manifolds $O (n ₁ + . . . + n_{q}) / O (n ₁) \times . . . \times O (n_{q})$ , q ≥ 3. We also give, or describe ways to obtain, interesting estimates for the cup-length of any $O (n ₁ + . . . + n_{q}) / O (n ₁) \times . . . \times O (n_{q})$ , q ≥ 3. To present another approach (combining well with the “method of fiberings”), we generalize to the real flag manifolds Stong’s approach used for calculations in the ℤ₂-cohomology algebra of the Grassmann manifolds.

Holonomy groups of complete flat manifolds

Michał Sadowski (2007)

Banach Center Publications

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We present short direct proofs of two known properties of complete flat manifolds. They say that the diffeomorphism classes of m-dimensional complete flat manifolds form a finite set $S_{C F} (m)$ and that each element of $S_{C F} (m)$ is represented by a manifold with finite holonomy group.

Overconvergent modular forms

Vincent Pilloni (2013)

Annales de l’institut Fourier

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We give a geometric definition of overconvergent modular forms of any $p$ -adic weight. As an application, we reprove Coleman’s theory of $p$ -adic families of modular forms and reconstruct the eigencurve of Coleman and Mazur without using the Eisenstein family.

Riemannian regular $σ$ -manifolds

A. A. Ermolitski (1994)

Czechoslovak Mathematical Journal

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Gauss–Manin connections for $p$ -adic families of nearly overconvergent modular forms

Robert Harron, Liang Xiao (2014)

Annales de l’institut Fourier

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We interpolate the Gauss–Manin connection in $p$ -adic families of nearly overconvergent modular forms. This gives a family of Maass–Shimura type differential operators from the space of nearly overconvergent modular forms of type $r$ to the space of nearly overconvergent modular forms of type $r + 1$ with $p$ -adic weight shifted by $2$ . Our construction is purely geometric, using Andreatta–Iovita–Stevens and Pilloni’s geometric construction of eigencurves, and should thus generalize to higher rank...

Bounds on sup-norms of half-integral weight modular forms

Eren Mehmet Kıral (2014)

Acta Arithmetica

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Bounding sup-norms of modular forms in terms of the level has been the focus of much recent study. In this work the sup-norm of a half-integral weight cusp form is bounded in terms of the level: we prove that $| | y^{κ / 2} {f ̃ | |}_{\infty} ≪_{ε, κ} N^{1 / 2 - 1 / 18 + ε} | | y^{κ / 2} f ̃ {| |}_{L^{2}}$ for a modular form f̃ of level 4N and weight κ, a half-integer.

On the variational calculus in fibered-fibered manifolds

W. M. Mikulski (2006)

Annales Polonici Mathematici

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In this paper we extend the variational calculus to fibered-fibered manifolds. Fibered-fibered manifolds are surjective fibered submersions π:Y → X between fibered manifolds. For natural numbers s ≥ r ≤ q with r ≥ 1 we define (r,s,q)th order Lagrangians on fibered-fibered manifolds π:Y → X as base-preserving morphisms $λ : J^{r, s, q} Y \to ⋀^{d i m X} T * X$ . Then similarly to the fibered manifold case we define critical fibered sections of Y. Setting p=max(q,s) we prove that there exists a canonical “Euler” morphism $(λ) : J^{r + s, 2 s, r + p} Y \to * Y \otimes ⋀^{d i m X} T * X$ of...

Global integral formulas for solving the $\bar{\partial}$ -equation on Stein manifolds

Gennadi M. Henkin, Jürgen Leiterer (1981)

Annales Polonici Mathematici

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Admissibly integral manifolds for semilinear evolution equations

Nguyen Thieu Huy, Vu Thi Ngoc Ha (2014)

Annales Polonici Mathematici

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We prove the existence of integral (stable, unstable, center) manifolds of admissible classes for the solutions to the semilinear integral equation $u (t) = U (t, s) u (s) + \int_{s}^{t} U (t, ξ) f (ξ, u (ξ)) d ξ$ when the evolution family ${(U (t, s))}_{t \geq s}$ has an exponential trichotomy on a half-line or on the whole line, and the nonlinear forcing term f satisfies the (local or global) φ-Lipschitz conditions, i.e., ||f(t,x)-f(t,y)|| ≤ φ(t)||x-y|| where φ(t) belongs to some classes of admissible function spaces. These manifolds are formed by trajectories of the...

Approximation results for nonlinear integral operators in modular spaces and applications

Ilaria Mantellini, Gianluca Vinti (2003)

Annales Polonici Mathematici

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We obtain modular convergence theorems in modular spaces for nets of operators of the form $(T_{w} f) (s) = \int_{H} K_{w} (s - h_{w} (t), f (h_{w} (t))) d μ_{H} (t)$ , w > 0, s ∈ G, where G and H are topological groups and ${h_{w}}_{w > 0}$ is a family of homeomorphisms $h_{w} : H \to h_{w} (H) \subset G .$ Such operators contain, in particular, a nonlinear version of the generalized sampling operators, which have many applications in the theory of signal processing.

On the Euler Function on Differences Between the Coordinates of Points on Modular Hyperbolas

Igor E. Shparlinski (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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For a prime p > 2, an integer a with gcd(a,p) = 1 and real 1 ≤ X,Y < p, we consider the set of points on the modular hyperbola $_{a, p} (X, Y) = (x, y) : x y \equiv a (m o d p), 1 \leq x \leq X, 1 \leq y \leq Y$ . We give asymptotic formulas for the average values $\sum_{\begin{matrix} ( \end{matrix} x, y) \in_{a, p} (X, Y) x \neq y *} φ (| x - y |) / | x - y |$ and $\sum_{\begin{matrix} ( \end{matrix} x, y) \in_{a, p} (X, X) x \neq y *} φ (| x - y |)$ with the Euler function φ(k) on the differences between the components of points of $_{a, p} (X, Y)$ .

Pseudosymmetric and Weyl-pseudosymmetric $(κ, μ)$ -contact metric manifolds

N. Malekzadeh, E. Abedi, U.C. De (2016)

Archivum Mathematicum

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In this paper we classify pseudosymmetric and Ricci-pseudosymmetric $(κ, μ)$ -contact metric manifolds in the sense of Deszcz. Next we characterize Weyl-pseudosymmetric $(κ, μ)$ -contact metric manifolds.

Dimensions of spaces of modular forms for $Γ_{H} (N)$

Jordi Quer (2010)

Acta Arithmetica

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Local Indecomposability of Hilbert Modular Galois Representations

Bin Zhao (2014)

Annales de l’institut Fourier

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We prove the indecomposability of the Galois representation restricted to the $p$ -decomposition group attached to a non CM nearly $p$ -ordinary weight two Hilbert modular form over a totally real field $F$ under the assumption that either the degree of $F$ over $ℚ$ is odd or the automorphic representation attached to the Hilbert modular form is square integrable at some finite place of $F$ .