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A p-adic approach to the Weil representation of discriminant forms arising from even lattices
Springer Science and Business Media LLC - Tập 39 - Trang 61-89 - 2015
Suppose that M is an even lattice with dual $$M^{*}$$ and level N. Then the
group $$Mp_{2}(\mathbb {Z})$$ , which is the unique non-trivial double cover of
$$SL_{2}(\mathbb {Z})$$ , admits a representation $$\rho _{M}$$ , called the
Weil representation, on the space $$\mathbb {C}[M^{*}/M]$$ . The main aim of
this paper is to show how the formulae for the $$\rho _{M}$$ -action of a
general element ...
Optimal bounds for Neumann eigenvalues in terms of the diameter
Springer Science and Business Media LLC -
Weighted Hodge cohomology of iterated fibred cusp metrics
Springer Science and Business Media LLC - Tập 39 Số 2 - Trang 177-184 - 2015
Square-full numbers in Piatetski–Shapiro sequences
Springer Science and Business Media LLC - Tập 44 Số 2 - Trang 385-391 - 2020
A p-adic Maass–Shimura operator on Mumford curves
Springer Science and Business Media LLC - Tập 47 Số 1 - Trang 139-175 - 2023
AbstractWe study a p-adic Maass–Shimura operator in the context of Mumford
curves defined by [15]. We prove that this operator arises from a splitting of
the Hodge filtration, thus answering a question in [15]. We also study the
relation of this operator with generalized Heegner cycles, in the spirit of [1,
4, 19, 28].
Aut-invariant quasimorphisms on free products
Springer Science and Business Media LLC - Tập 47 - Trang 475-493 - 2021
Let $$G=A *B$$ be a free product of freely indecomposable groups. We explicitly
construct quasimorphisms on G which are invariant with respect to all
automorphisms of G. We also prove that the space of such quasimorphisms is
infinite-dimensional whenever G is not the infinite dihedral group. As an
application we prove that an invariant analogue of stable commutator length
recently introduced by Ka...
On abelian $$\ell $$ -towers of multigraphs
Springer Science and Business Media LLC - Tập 45 - Trang 433-452 - 2021
We study how the $$\ell $$ -adic valuation of the number of spanning trees
varies in regular abelian $$\ell $$ -towers of multigraphs. We show that for an
infinite family of regular abelian $$\ell $$ -towers of bouquets, the $$\ell $$
-adic valuation of the number of spanning trees behaves similarly to the $$\ell
$$ -adic valuation of the class numbers in $${\mathbb {Z}}_{\ell }$$ -extensions
of n...
On adjoint Bloch–Kato Selmer groups for $$\textrm{GSp}_{2g}$$
Springer Science and Business Media LLC - - Trang 1-34 - 2022
We study the adjoint Bloch–Kato Selmer groups attached to a classical point in
the cuspidal eigenvariety associated with $$\textrm{GSp}_{2g}$$ . Our strategy
is based on the study of families of Galois representations on the eigenvariety,
which is inspired by the book of J. Bellaiche and G. Chenevier.
On the number of cusps of orthogonal Shimura varieties
Springer Science and Business Media LLC - Tập 38 - Trang 119-131 - 2014
We study the cusps of Shimura varieties arising from indefinite lattices
splitting two hyperbolic planes. We determine the number of 0-dimensional cusps
for a given variety and, when the lattice is maximal, we relate the genus of the
lattice to the number of $$1$$ -dimensional cusps and determine an explicit
formula. As every lattice is contained as a sublattice of finite index in a
maximal lattic...
Régularité höldérienne des schémas de subdivision et des fonctions vectorielles d’échelle
Springer Science and Business Media LLC - Tập 39 - Trang 91-112 - 2015
Nous reprenons le modèle de Buhmann et de Micchelli de schémas périodiques de
subdivision à une variable. À chacun de ces schémas, sont associées deux
équations fonctionnelles donnant lieu à la notion de fonction vectorielle
d’échelle. L’étude de la régularité holdérienne des schémas de subdivision se
réduit alors à celle de la régularité des fonctions vectorielles d’échelle.
L’existence d’une sol...
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