547 research outputs found
Dichotomy for generic supercuspidal representations of
The local Langlands conjectures imply that to every generic supercuspidal
irreducible representation of over a -adic field, one can associate a
generic supercuspidal irreducible representation of either or.
We prove this conjectural dichotomy, demonstrating a precise correspondence
between certain representations of and other representations of
and . This correspondence arises from theta correspondences in and
, analysis of Shalika functionals, and spin L-functions. Our main result
reduces the conjectural Langlands parameterization of generic supercuspidal
irreducible representations of to a single conjecture about the
parameterization for .Comment: Version 2: Mistakes in Prop 3.2 and 3.5 corrected. Results
strengthened in case p=2. Changes made throughout for consistency with
stronger results and reformulatio
Osmotic force resisting chain insertion in a colloidal suspension
We consider the problem of inserting a stiff chain into a colloidal
suspension of particles that interact with it through excluded volume forces.
The free energy of insertion is associated with the work of creating a cavity
devoid of colloid and sufficiently large to accomodate the chain. The
corresponding work per unit length is the force that resists the entry of the
chain into the colloidal suspension. In the case of a hard sphere fluid, this
work can be calculated straightforwardly within the scaled particle theory; for
solutions of flexible polymers, on the other hand, we employ simple scaling
arguments. The forces computed in these ways are shown, for nanometer chain and
colloid diameters, to be of the order of tens of pN for solution volume
fraction for biophysical processes such as the ejection of DNA from viral
capsids into the cell cytoplasm.Comment: 16 pages,3 figures. Accepted for publication in European Physical
Journal
Electrostatic complexation of spheres and chains under elastic stress
We consider the complexation of highly charged semiflexible polyelectrolytes
with oppositely charged macroions. On the basis of scaling arguments we discuss
how the resulting complexes depend on the persistence length of the
polyelectrolyte, the salt concentration, and the sizes and charges of the chain
and the macroions. We study first the case of complexation with a single sphere
and calculate the wrapping length of the chain. We then extend our
considerations to complexes involving many wrapped spheres and study
cooperative effects. The mechanical properties of such a complex under an
external deformation are evaluated.Comment: 16 pages, submitted to J. Chem. Phy
Hybrid bounds for twisted L-functions
The aim of this paper is to derive bounds on the critical line Rs 1/2 for L- functions attached to twists f circle times chi of a primitive cusp form f of level N and a primitive character modulo q that break convexity simultaneously in the s and q aspects. If f has trivial nebentypus, it is shown that
L(f circle times chi, s) << (N vertical bar s vertical bar q)(epsilon) N-4/5(vertical bar s vertical bar q)(1/2-1/40),
where the implied constant depends only on epsilon > 0 and the archimedean parameter of f. To this end, two independent methods are employed to show
L(f circle times chi, s) << (N vertical bar s vertical bar q)(epsilon) N-1/2 vertical bar S vertical bar(1/2)q(3/8) and
L(g,s) << D-2/3 vertical bar S vertical bar(5/12)
for any primitive cusp form g of level D and arbitrary nebentypus (not necessarily a twist f circle times chi of level D vertical bar Nq(2))
Organized condensation of worm-like chains
We present results relevant to the equilibrium organization of DNA strands of
arbitrary length interacting with a spherical organizing center, suggestive of
DNA-histone complexation in nucleosomes. We obtain a rich phase diagram in
which a wrapping state is transformed into a complex multi-leafed, rosette
structure as the adhesion energy is reduced. The statistical mechanics of the
"melting" of a rosette can be mapped into an exactly soluble one-dimensional
many-body problem.Comment: 15 pages, 2 figures in a pdf fil
Bounding sup-norms of cusp forms of large level
Let f be an -normalized weight zero Hecke-Maass cusp form of square-free
level N, character and Laplacian eigenvalue . It is
shown that , from which the hybrid
bound (for some
) is derived. The first bound holds also for where F
is a holomorphic cusp form of weight k with the implied constant now depending
on k.Comment: version 3: substantially revised versio
What do emulsification failure and Bose-Einstein condensation have in common?
Ideal bosons and classical ring polymers formed via self-assembly, are known
to have the same partition function, and so analogous phase transitions. In
ring polymers, the analogue of Bose-Einstein condensation occurs when a ring
polymer of macroscopic size appears. We show that a transition of the same
general form occurs within a whole class of systems with self-assembly, and
illustrate it with the emulsification failure of a microemulsion phase of
water, oil and surfactant. As with Bose-Einstein condensation, the transition
occurs even in the absence of interactions.Comment: 7 pages, 1 figure, typeset with EUROTeX, uses epsfi
Distinguished non-Archimedean representations
For a symmetric space (G,H), one is interested in understanding the vector
space of H-invariant linear forms on a representation \pi of G. In particular
an important question is whether or not the dimension of this space is bounded
by one. We cover the known results for the pair (G=R_{E/F}GL(n),H=GL(n)), and
then discuss the corresponding SL(n) case. In this paper, we show that
(G=R_{E/F}SL(n),H=SL(n)) is a Gelfand pair when n is odd. When is even, the
space of H-invariant forms on \pi can have dimension more than one even when
\pi is supercuspidal. The latter work is joint with Dipendra Prasad
Mass equidistribution of Hilbert modular eigenforms
Let F be a totally real number field, and let f traverse a sequence of
non-dihedral holomorphic eigencuspforms on GL(2)/F of weight (k_1,...,k_n),
trivial central character and full level. We show that the mass of f
equidistributes on the Hilbert modular variety as max(k_1,...,k_n) tends to
infinity.
Our result answers affirmatively a natural analogue of a conjecture of
Rudnick and Sarnak (1994). Our proof generalizes the argument of
Holowinsky-Soundararajan (2008) who established the case F = Q. The essential
difficulty in doing so is to adapt Holowinsky's bounds for the Weyl periods of
the equidistribution problem in terms of manageable shifted convolution sums of
Fourier coefficients to the case of a number field with nontrivial unit group.Comment: 40 pages; typos corrected, nearly accepted for
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