131 research outputs found
Epsilon factors as algebraic characters on the smooth dual of
Let be a non-archimedean local field and let . We
have shown in previous work that the smooth dual admits a
complex structure: in this article we show how the epsilon factors interface
with this complex structure. The epsilon factors, up to a constant term, factor
as invariant characters through the corresponding complex tori. For the
arithmetically unramified smooth dual of , we provide explicit
formulas for the invariant characters.Comment: 12 pages. Minor improvements, new titl
Base change and K-theory for GL(n,R)
We investigate base change at the level of -theory for the general
linear group . In the course of this study, we compute in detail the
-algebra -theory of this disconnected group. We investigate the
interaction of base change with the Baum-Connes correspondence for
and . This article is the archimedean companion of our previous
article in the Journal of Noncommutative Geometry.Comment: 17 pages, introduction and section 5 completely rewritte
Base change and K-theory for GL(n)
Let F be a nonarchimedean local field and let G = GL(n) = GL(n,F). Let E/F be
a finite Galois extension. We investigate base change E/F at two levels: at the
level of algebraic varieties, and at the level of K-theory. We put special
emphasis on the representations with Iwahori fixed vectors, and the tempered
spectrum of GL(1) and GL(2). In this context, the prominent arithmetic
invariant is the residue degree f(E/F).Comment: 20 pages. Completely rewritten, much more concis
L-packets and depth for SL_2(K) with K a local function field of characteristic 2
Let G = SL_2(K) with K a local function field of characteristic 2. We review
Artin-Schreier theory for the field K, and show that this leads to a
parametrization of certain L-packets in the smooth dual of G. We relate this to
a recent geometric conjecture. The L-packets in the principal series are
parametrized by quadratic extensions, and the supercuspidal L-packets of
cardinality 4 are parametrized by biquadratic extensions. Each supercuspidal
packet of cardinality 4 is accompanied by a singleton packet for SL_1(D). We
compute the depths of the irreducible constituents of all these L-packets for
SL_2(K) and its inner form SL_1(D).Comment: 18 pages. arXiv admin note: substantial text overlap with
arXiv:1302.603
K-theory and the connection index
Let G denote a split simply connected almost simple p-adic group. The
classical example is the special linear group SL(n). We study the K-theory of
the unramified unitary principal series of G and prove that the rank of K_0 is
the connection index f(G). We relate this result to a recent refinement of the
Baum-Connes conjecture, and show explicitly how generators of K_0 contribute to
the K-theory of the Iwahori C*-algebra I(G).Comment: 11 page
A new bound for the smallest with
We reduce the leading term in Lehman's theorem. This improved estimate allows
us to refine the main theorem of Bays and Hudson. Entering Riemann
zeros, we prove that there exists in the interval for which \pi(x)-\li(x) > 3.2 \times 10^{151}. There are at
least successive integers in this interval for which
\pi(x)>\li(x). This interval is strictly a sub-interval of the interval in
Bays and Hudson, and is narrower by a factor of about 12.Comment: Final version, to be published in the International Journal of Number
Theory [copyright World Scientific Publishing
Company][www.worldscinet.com/ijnt
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