Project MUSE®: American Journal of Mathematics - Latest Articles
https://muse.jhu.edu/journals/american_journal_of_mathematics
Project MUSE®: Latest articles in American Journal of Mathematics.daily12016-02-10T04:00:30-05:00text/htmlen-USThe Johns Hopkins University PressVol. 118 (1996) through current issueLatest Articles: American Journal of MathematicsMathematicsTWOProject MUSE®American Journal of Mathematics1080-63770002-9327Latest articles in American Journal of Mathematics. Feed provided by Project MUSE®Motivic height zeta functions
https://muse.jhu.edu/journals/american_journal_of_mathematics/v138/138.1.chambert-loir.html
<p>By Antoine Chambert-Loir, François Loeser</p>
We consider a motivic analogue of the height zeta function for integral points of equivariant partial compactifications of affine spaces. We establish its rationality and determine its largest ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v138/138.1.chambert-loir.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2016-02-10T04:00:30-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgMotivic height zeta functions2016-02-09text/htmlen-USThe Johns Hopkins University PressMotivic height zeta functions2016-02-092016TWOProject MUSE®02016-02-09T00:00:00-05:002016-02-09Bounds for p-adic exponential sums and log-canonical thresholds
https://muse.jhu.edu/journals/american_journal_of_mathematics/v138/138.1.cluckers.html
<p>By Raf Cluckers, Willem Veys</p>
We propose a conjecture for exponential sums which generalizes both a conjecture by Igusa and a local variant by Denef and Sperber, in particular, it is without the homogeneity condition on the polynomial in the phase, and with new predicted uniform behavior. The exponential sums have summation sets consisting of integers modulo pm lying p-adically close to y, and the proposed bounds are uniform in p, y, and m. We give evidence for the conjecture, by showing uniform bounds in p, y, and in some values for m. On the way, we prove new bounds for log-canonical thresholds which are closely related to the bounds predicted by the ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v138/138.1.cluckers.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2016-02-10T04:00:30-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgBounds for p-adic exponential sums and log-canonical thresholds2016-02-09text/htmlen-USThe Johns Hopkins University PressBounds for p-adic exponential sums and log-canonical thresholds2016-02-092016TWOProject MUSE®02016-02-09T00:00:00-05:002016-02-09On the formal arc space of a reductive monoid
https://muse.jhu.edu/journals/american_journal_of_mathematics/v138/138.1.bouthier.html
<p>By A. Bouthier, B. C. Ngô, Y. Sakellaridis</p>
Let X be a scheme of finite type over a finite field k, and let LX denote its arc space; in particular, LX(k) = X(k[[t]]). Using the theory of Grinberg, Kazhdan, and Drinfeld on the finite-dimensionality of singularities of LX in the neighborhood of non-degenerate arcs, we show that a canonical “basic function” can be defined on the non-degenerate locus of LX(k), which corresponds to the trace of Frobenius on the stalks of the intersection complex of any finite-dimensional model. We then proceed to compute this function when X is an affine toric variety or an “L-monoid”. Our computation confirms the expectation that the basic function is a generating function for a local un-ramified L-function; in particular, in ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v138/138.1.bouthier.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2016-02-10T04:00:30-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgOn the formal arc space of a reductive monoid2016-02-09text/htmlen-USThe Johns Hopkins University PressOn the formal arc space of a reductive monoid2016-02-092016TWOProject MUSE®02016-02-09T00:00:00-05:002016-02-09Endoscopic transfer of orbital integrals in large residual characteristic
https://muse.jhu.edu/journals/american_journal_of_mathematics/v138/138.1.gordon.html
<p>By Julia Gordon, Thomas Hales</p>
This article constructs Shalika germs in the context of motivic integration, both for ordinary orbital integrals and κ-orbital integrals. Based on transfer principles in motivic integration and on Waldspurger’s endoscopic transfer of smooth functions in characteristic zero, we deduce the endoscopic transfer of smooth functions in sufficiently large residual ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v138/138.1.gordon.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2016-02-10T04:00:30-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgEndoscopic transfer of orbital integrals in large residual characteristic2016-02-09text/htmlen-USThe Johns Hopkins University PressEndoscopic transfer of orbital integrals in large residual characteristic2016-02-092016TWOProject MUSE®02016-02-09T00:00:00-05:002016-02-09A survey of Igusa’s local zeta function
https://muse.jhu.edu/journals/american_journal_of_mathematics/v138/138.1.meuser.html
<p>By Diane Meuser</p>
The origin and development of the Igusa local zeta function, by Igusa and others, is presented. In particular, we discuss the various conjectures Igusa made and the notable results that have so far been obtained. We also explain how topological and motivic zeta functions arose from the Igusa local zeta function and present the current status of the analogous conjectures. Igusa’s conjecture on exponential sums that are related to his zeta function is described, and along with the progress made towards its ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v138/138.1.meuser.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2016-02-10T04:00:30-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgA survey of Igusa’s local zeta function2016-02-09text/htmlen-USThe Johns Hopkins University PressA survey of Igusa’s local zeta functionIgusa, Jun-ichi,2016-02-092016TWOProject MUSE®02016-02-09T00:00:00-05:002016-02-09Geometric proofs of theorems of Ax-Kochen and Eršov
https://muse.jhu.edu/journals/american_journal_of_mathematics/v138/138.1.denef.html
<p>By Jan Denef</p>
We give an algebraic geometric proof of the Theorem of Ax and Kochen on p-adic diophantine equations in many variables. Unlike Ax-Kochen’s proof, ours does not use any notions from mathematical logic and is based on weak toroidalization of morphisms. We also show how this geometric approach yields new proofs of the Ax-Kochen-Eršov transfer principle for local fields, and of quantifier elimination theorems of Basarab and ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v138/138.1.denef.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2016-02-10T04:00:30-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgGeometric proofs of theorems of Ax-Kochen and Eršov2016-02-09text/htmlen-USThe Johns Hopkins University PressGeometric proofs of theorems of Ax-Kochen and Eršov2016-02-092016TWOProject MUSE®02016-02-09T00:00:00-05:002016-02-09On a conjecture of Igusa II
https://muse.jhu.edu/journals/american_journal_of_mathematics/v138/138.1.lichtin.html
<p>By Ben Lichtin</p>
In his 1978 Tata Lecture Notes, Igusa conjectured the validity of a strong uniformity in the decay of complete exponential sums modulo powers of a prime number and determined by a homogeneous polynomial. We prove this property for absolutely reduced ternary ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v138/138.1.lichtin.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2016-02-10T04:00:30-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgOn a conjecture of Igusa II2016-02-09text/htmlen-USThe Johns Hopkins University PressOn a conjecture of Igusa IIIgusa, Jun-ichi,2016-02-092016TWOProject MUSE®02016-02-09T00:00:00-05:002016-02-09Homotopy groups of Chow varieties
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.6.hu.html
<p>By Wenchuan Hu</p>
We show that a conjecture by Lawson holds, that is, the inclusion from the Chow variety Cp,d(ℙn) of all effective algebraic p-cycles of degree d in n-dimensional projective space ℙn to the space Cp(ℙn) of effective algebraic p-cycles in ℙn is 2d-connected. As a result, the homotopy and homology groups of Cp,d(ℙn) are calculated up to 2d. We also obtain the homotopy groups up to a certain level for the space of algebraic cycles with a fixed ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.6.hu.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2016-02-10T04:00:30-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgHomotopy groups of Chow varieties2015-11-30text/htmlen-USThe Johns Hopkins University PressHomotopy groups of Chow varieties2015-11-302015TWOProject MUSE®02015-11-30T00:00:00-05:002015-11-30The local Langlands correspondence for GSp4 over local function fields
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.6.ganapathy.html
<p>By Radhika Ganapathy</p>
We prove the local Langlands correspondence for GSp4(F), where F is a non-archimedean local field of positive characteristic with residue characteristic > ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.6.ganapathy.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2016-02-10T04:00:30-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgThe local Langlands correspondence for GSp4 over local function fields2015-11-30text/htmlen-USThe Johns Hopkins University PressThe local Langlands correspondence for GSp4 over local function fields2015-11-302015TWOProject MUSE®02015-11-30T00:00:00-05:002015-11-30Directional maximal operators and lacunarity in higher dimensions
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.6.parcet.html
<p>By Javier Parcet, Keith M. Rogers</p>
We introduce a notion of lacunarity in higher dimensions for which we can bound the associated directional maximal operators in Lp(ℝn), with p > 1. In particular, we are able to treat the classes previously considered by Nagel-Stein-Wainger, Sjögren-Sjölin and Carbery. Closely related to this, we find a characterization of the sets of directions which give rise to bounded maximal operators. The bounds enable Lebesgue-type differentiation of integrals in (ℝn), replacing balls by tubes which point in these ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.6.parcet.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2016-02-10T04:00:30-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgDirectional maximal operators and lacunarity in higher dimensions2015-11-30text/htmlen-USThe Johns Hopkins University PressDirectional maximal operators and lacunarity in higher dimensions2015-11-302015TWOProject MUSE®02015-11-30T00:00:00-05:002015-11-30