integrable modules for affine lie superalgebras irreducible nonzero level modules with finite dimensional weight spaces are discussed for nontwisted affine lie superalgebras a complete classification of such modules is obtained for superalgebras of type a m n and c n using mathieu s classification of cuspidal modules over simple lie algebras in other cases the classification problem is reduced to the classification of cuspidal modules over finite dimensional cuspidal lie superalgebras described by dimitrov mathieu and penkov based on these results a complete classification of irreducible integrable in the sense of kac and wakimoto modules is obtained by showing that any such module is of highest weight in which case the problem was solved by kac and wakimoto

the l component of the unipotent albanese map we prove a finiteness theorem for the local l p component of the qp unipotent albanese map for curves as an application we refine the non abelian selmer varieties arising in the study of global points and deduce thereby a new proof of siegel s theorem for affine curves over q of genus one with mordell weil rank at most one

solving discrete zero point problems in this paper we present two theorems on the existence of a discrete zero point of a function from the n dimensional integer lattice n to the n dimensional euclidean space n the theorems differ in their boundary conditions for both theorems we give a proof using a combinatorial lemma and present a constructive proof based on a simplicial algorithm that finds a discrete zero point within a finite number of steps

a non abelian conjecture of tate shafarevich type for hyperbolic curves let x denote a hyperbolic curve over mathbb q and let p denote a prime of good reduction the third author s approach to integral points introduced in kim invent math 161 629 656 2005 publ res inst math sci 45 89 133 2009 endows x mathbb z p with a nested sequence of subsets x mathbb z p n which contain x mathbb z these sets have been computed in a range of special cases balakrishnan et al j am math soc 24 281 291 2011 dan cohen and wewers proc lond math soc 110 133 171 2015 dan cohen and wewers int math res not imrn 17 5291 5354 2016 kim j am math soc 23 725 747 2010 there is good reason to believe them to be practically computable in general in 2012 the third author announced the conjecture that for n sufficiently large x mathbb z x mathbb z p n this conjecture may be seen as a sort of compromise between the abelian confines of the bsd conjecture and the profinite world of the grothendieck section conjecture after stating the conjecture and explaining its relationship to these other conjectures we explore a range of special cases in which the new conjecture can be verified

non vanishing of high derivatives of automorphic l functions at the center of the critical strip keywords modular l functions mollification nonvanishing results central value of high derivatives analytic rank jacobian variety reference tan article 2000 004doi 10 1515 crll 2000 074 record created on 2008 11 14 modified on 2017 05 12

surjectivity of galois representations associated with quadratic mathbb q curves we prove in this paper an uniform surjectivity result for galois representations associated with non cm mathbb q curves over imaginary quadratic fields using various tools for the proof such as mazur s method isogeny theorems runge s method and analytic estimates of sums of l functions

galois representations attached to q curves and the generalized fermat equation a 4 b 2 c p we prove that the equation a 4 b 2 c p has no solutions in coprime positive integers when p 211 the main step is to show that for all sufficiently large primes p every q curve over an imaginary quadratic field k with a prime of potentially multiplicative reduction greater than 6 has a surjective mod p galois representation the bound on p depends on k and the degree of the isogeny between e and its galois conjugate but is independent of the choice of e the proof of this theorem combines geometric arguments due to mazur momose darmon and merel with an analytic estimate of the average special values of certain l functions

tests of risk premia in linear factor models abstract we show that statistical inference on the risk premia in linear factor models that is based on the fama macbeth fm and generalized least squares gls two pass risk premia estimators is misleading when the s are small and or the number of assets is large we propose novel statistics that are based on the maximum likelihood estimator of gibbons gibbons m 1982 multivariate tests of financial models a new approach journal of financial economics 10 3 27 which remain trustworthy in these cases the inadequacy of the fm and gls two pass t wald statistics is highlighted in a power and size comparison using quarterly portfolio returns from lettau and ludvigson lettau m ludvigson s 2001 resurrecting the c capm a cross sectional test when risk premia are time varying journal of political economy 109 1238 1287 the power and size comparison shows that the fm and gls two pass t wald statistics can be severely size distorted the 95 confidence sets for the risk premia in the above cited work that result from the novel statistics differ substantially from those that result from the fm and gls two pass t statistics they show support for the human capital asset pricing model although the 95 confidence set for the risk premia on labor income growth is unbounded the 95 confidence sets show no support for the scaled consumption asset pricing model since the 95 confidence set of the risk premia on the scaled consumption growth consists of the whole real line but do not reject it either

on the structure of weight modules given any simple lie superalgebra g we investigate the structure of an arbitrary simple weight 0 module we introduce two invariants of simple weight modules the shadow and the small weyl group generalizing results of fernando and futorny we show that any simple module is obtained by parabolic induction from a cuspidal module of a levi subsuperalgebra then we classify the cuspidal levi subsuperalgebras of all simple classical lie superalgebras and of the lie superalgebra w n most of them are simply levi subalgebras of go in which case the classification of all finite cuspidal representations has recently been carried out by one of us mathieu our results reduce the classification of the finite simple weight modules over all classical simple lie superalgebras to classifying the finite cuspidal modules over certain lie superalgebras which we list explicitly

quadratic chabauty for modular curves and modular forms of rank one in this paper we provide refined sufficient conditions for the quadratic chabauty method on a curve x to produce an effective finite set of points containing the rational points x mathbb q with the condition on the rank of the jacobian of x replaced by condition on the rank of a quotient of the jacobian plus an associated space of chow heegner points we then apply this condition to prove the effective finiteness of x mathbb q for any modular curve x x 0 n or x mathrm ns n of genus at least 2 with n prime the proof relies on the existence of a quotient of their jacobians whose mordell weil rank is equal to its dimension and at least 2 which is proven via analytic estimates for orders of vanishing of l functions of modular forms thanks to a kolyvagin logachev type result

finite weight modules over twisted affine lie superalgebras abstract this work provides the first step toward the classification of irreducible finite weight modules over twisted affine lie superalgebras we divide the class of such modules into two subclasses called hybrid and tight we reduce the classification of hybrid irreducible finite weight modules to the classification of cuspidal modules of finite dimensional cuspidal lie superalgebras which is discussed in a work of dimitrov mathieu and penkov

unexplained factors and their effects on second pass r squared s we construct the large sample distributions of the ols and gls r2r2 s of the second pass regression of the fama and macbeth 1973 two pass procedure when the observed proxy factors are minorly correlated with the true unobserved factors this implies an unexplained factor structure in the first pass residuals and consequently a large estimation error in the estimated beta s which is spanned by the beta s of the unexplained true factors the average portfolio returns and the estimation error of the estimated beta s are then both linear in the beta s of the unobserved true factors which leads to possibly large values of the ols r2r2 of the second pass regression these large values of the ols r2r2 are not indicative of the strength of the relationship our results question many empirical findings that concern the relationship between expected portfolio returns and macro economic factors

on relations between jacobians of certain modular curves abstract we confirm a conjecture of l merel h darmon and l merel j reine angew math 490 1997 81 100 describing a certain relation between the jacobians of various quotients of x p in terms of specific correspondences the method of proof involves reducing this conjecture to a question about certain z gl 2 f p module homomorphisms which is in turn answered by exhibiting some peculiar relations in a double coset algebra

integrable highest weight modules over affine superalgebras and appell s function we classify integrable irreducible highest weight representations of non twisted affine lie superalgebras we give a free field construction in the level 1 case the analysis of this construction shows in particular that in the simplest case of the sl 2 1 level 1 affine superalgebra the characters are expressed in terms of the appell elliptic function our results demonstrate that the representation theory of affine lie superalgebras is quite different from that of affine lie algebras

classification of irreducible nonzero level modules with finite dimensional weight spaces for affine lie algebras abstract we classify the irreducible weight affine lie algebra modules with finite dimensional weight spaces on which the central element acts nontrivially in particular we show that any such module is a quotient of a generalized verma module the classification of such irreducible modules is reduced to the classification of irreducible torsion free modules for algebras of type a n and c n which is due to o mathieu forthcoming

lie algebra modules with finite dimensional weight spaces i let g denote a reductive lie algebra over an algebraically closed field of characteristic zero and let 4 denote a cartan subalgebra of g in this paper we study finitely generated g modules that decompose into direct sums of finite dimensional 4 weight spaces we show that the classification of irreducible modules in this category can be reduced to the classification of a certain class of irreducible modules those we call torsion free modules we also show that if g is a simple lie algebra that admits a torsion free module then g is of type a or c

serre s uniformity problem in the split cartan case we prove that there exists an integer p 0 such that x split p q is made of cusps and cm points for any prime p p 0 equivalently for any non cm elliptic curve e over q and any prime p p 0 the image of the galois representation induced by the galois action on the p division points of e is not contained in the normalizer of a split cartan subgroup this gives a partial answer to an old question of serre

explicit chabauty kim for the split cartan modular curve of level 13 we extend the explicit quadratic chabauty methods developed in previous work by the first two authors to the case of non hyperelliptic curves this results in an algorithm to compute the rational points on a curve of genus g 2 over the rationals whose jacobian has mordell weil rank g and picard number greater than one and which satisfies some additional conditions this algorithm is then applied to the modular curve x s 13 completing the classification of non cm elliptic curves over q with split cartan level structure due to bilu parent and bilu parent rebolledo

asymptotics of the principal components estimator of large factor models with weakly influential factors abstract this paper introduces a drifting parameter asymptotic framework to derive accurate approximations to the finite sample distribution of the principal components pc estimator in situations when the factors explanatory power does not strongly dominate the explanatory power of the cross sectionally and temporally correlated idiosyncratic terms under our asymptotics the pc estimator is inconsistent we find explicit formulae for the amount of the inconsistency and propose an estimator of the number of factors for which the pc estimator works reasonably well for the special case when the idiosyncratic terms are cross sectionally but not temporally correlated or vice versa we show that the coefficients in the ols regressions of the pc estimates of factors loadings on the true factors true loadings are asymptotically normal and find explicit formulae for the corresponding asymptotic covariance matrix we explain how to estimate the parameters of the derived asymptotic distributions our monte carlo analysis suggests that our asymptotic formulae and estimators work well even for relatively small n and t we apply our theoretical results to test a hypothesis about the factor content of the us stock return data

the motivic fundamental group of p1 0 1 and the theorem of siegel in this paper we establish a link between the structure theory of the pro unipotent motivic fundamental group of the projective line minus three points and diophantine geometry in particular we give a p adic proof of siegel s theorem