77 research outputs found
Chronik des III. Internationalen Mathematiker-Kongresses in Heidelberg 1904
Die Deutsche Mathematiker-Vereinigung richtete 1904 den 3. Internationalen Mathematiker-Kongress in Heidelberg aus. Inhalt der Chronik: A. Vorgeschichte des Kongresses B. Programm des III. Internationalen Mathematiker-Kongresses C. Verzeichnis der Kongressmitglieder D. Verlauf des Kongresse
Ăber die Unendlichkeits- und Nullpunkte einer algebraischen Funktion
FaĂt man den allgemeinen Integranden I. Gattung als eine Linearform von p unabhĂ€ngigen VerĂ€nderlichen auf, so nehmen die Gleichungen zwischen den Unendlichkeitspunkten einer algebraischen Funktion und deren Gewichten eine besonders ĂŒbersichtliche Gestalt an und erschlieĂen einen tieferen Einblick in die Natur solcher Punktsysteme
The arithmetic of genus two curves with (4,4)-split Jacobians
In this paper we study genus 2 curves whose Jacobians admit a polarized
(4,4)-isogeny to a product of elliptic curves. We consider base fields of
characteristic different from 2 and 3, which we do not assume to be
algebraically closed. We obtain a full classification of all principally
polarized abelian surfaces that can arise from gluing two elliptic curves along
their 4-torsion and we derive the relation their absolute invariants satisfy.
As an intermediate step, we give a general description of Richelot isogenies
between Jacobians of genus 2 curves, where previously only Richelot isogenies
with kernels that are pointwise defined over the base field were considered.
Our main tool is a Galois theoretic characterization of genus 2 curves
admitting multiple Richelot isogenies.Comment: 30 page
General relativistic gravitational field of a rigidly rotating disk of dust: Solution in terms of ultraelliptic functions
In a recent paper we presented analytic expressions for the axis potential,
the disk metric, and the surface mass density of the global solution to
Einstein's field equations describing a rigidly rotating disk of dust. Here we
add the complete solution in terms of ultraelliptic functions and quadratures.Comment: 5 pages, published in 1995 [Phys. Rev. Lett. 75 (1995) 3046
Finite Temperature Correlators in the Schwinger Model
We discuss the correlation function of hadronic currents in the Schwinger
model at finite temperature . We explicitly construct the retarded
correlator in real time and obtain analytical results for the Euclidean
correlator on a torus. Both constructions lead to the same finite temperature
spectral function. The spatial screening lengths in the mesonic channels are
related to the dynamical meson mass and not even in
the infinite temperature limit. The relevance of our results for the finite
temperature problem in four dimensions is discussed.Comment: in LATEX, 30 pages; two figures available on request from the
authors; USITP-93-19, SUNY-NTG-43, (explanations to the figures have been
clarified
Closed geodesics and billiards on quadrics related to elliptic KdV solutions
We consider algebraic geometrical properties of the integrable billiard on a
quadric Q with elastic impacts along another quadric confocal to Q. These
properties are in sharp contrast with those of the ellipsoidal Birkhoff
billiards. Namely, generic complex invariant manifolds are not Abelian
varieties, and the billiard map is no more algebraic. A Poncelet-like theorem
for such system is known. We give explicit sufficient conditions both for
closed geodesics and periodic billiard orbits on Q and discuss their relation
with the elliptic KdV solutions and elliptic Calogero systemComment: 23 pages, Latex, 1 figure Postscrip
Alternating groups and moduli space lifting Invariants
Main Theorem: Spaces of r-branch point 3-cycle covers, degree n or Galois of
degree n!/2 have one (resp. two) component(s) if r=n-1 (resp. r\ge n). Improves
Fried-Serre on deciding when sphere covers with odd-order branching lift to
unramified Spin covers. We produce Hurwitz-Torelli automorphic functions on
Hurwitz spaces, and draw Inverse Galois conclusions. Example: Absolute spaces
of 3-cycle covers with +1 (resp. -1) lift invariant carry canonical even (resp.
odd) theta functions when r is even (resp. odd). For inner spaces the result is
independent of r. Another use appears in,
http://www.math.uci.edu/~mfried/paplist-mt/twoorbit.html, "Connectedness of
families of sphere covers of A_n-Type." This shows the M(odular) T(ower)s for
the prime p=2 lying over Hurwitz spaces first studied by,
http://www.math.uci.edu/~mfried/othlist-cov/hurwitzLiu-Oss.pdf, Liu and
Osserman have 2-cusps. That is sufficient to establish the Main Conjecture: (*)
High tower levels are general-type varieties and have no rational points.For
infinitely many of those MTs, the tree of cusps contains a subtree -- a spire
-- isomorphic to the tree of cusps on a modular curve tower. This makes
plausible a version of Serre's O(pen) I(mage) T(heorem) on such MTs.
Establishing these modular curve-like properties opens, to MTs, modular
curve-like thinking where modular curves have never gone before. A fuller html
description of this paper is at
http://www.math.uci.edu/~mfried/paplist-cov/hf-can0611591.html .Comment: To appear in the Israel Journal as of 1/5/09; v4 is corrected from
proof sheets, but does include some proof simplification in \S
Wannier functions for quasi-periodic finite-gap potentials
In this paper we consider Wannier functions of quasi-periodic g-gap () potentials and investigate their main properties. In particular, we discuss
the problem of averaging underlying the definition of Wannier functions for
both periodic and quasi-periodic potentials and express Bloch functions and
quasi-momenta in terms of hyperelliptic functions. Using this approach
we derive a power series expansion of the Wannier function for quasi-periodic
potentials valid at and an asymptotic expansion valid at large
distance. These functions are important for a number of applied problems
Superstring scattering amplitudes in higher genus
In this paper we continue the program pioneered by D'Hoker and Phong, and
recently advanced by Cacciatori, Dalla Piazza, and van Geemen, of finding the
chiral superstring measure by constructing modular forms satisfying certain
factorization constraints. We give new expressions for their proposed ans\"atze
in genera 2 and 3, respectively, which admit a straightforward generalization.
We then propose an ansatz in genus 4 and verify that it satisfies the
factorization constraints and gives a vanishing cosmological constant. We
further conjecture a possible formula for the superstring amplitudes in any
genus, subject to the condition that certain modular forms admit holomorphic
roots.Comment: Minor changes; final version to appear in Comm. Math. Phy
- âŠ