DSpace Community: KAIST Dept. of Mathematical SciencesKAIST Dept. of Mathematical Scienceshttp://hdl.handle.net/10203/5272018-05-04T09:19:30Z2018-05-04T09:19:30ZSingly periodic free boundary minimal surfaces in a solid cylinder of H-2 x RMorabito, Filippohttp://hdl.handle.net/10203/2414012018-04-24T06:32:14Z2018-06-01T00:00:00ZTitle: Singly periodic free boundary minimal surfaces in a solid cylinder of H-2 x R
Authors: Morabito, Filippo
Abstract: The aim of this work is to show there exist free boundary minimal surfaces of Saddle Tower type which are embedded in a vertical solid cylinder of H-2 x R, H-2 being the hyperbolic plane, and invariant under the action of a vertical translation and a rotation. The number of boundary curves equals 2l, l >= 2. These surfaces come in families depending on one parameter and they converge to 2l vertical stripes having a common intersection line. (c) 2018 Elsevier Ltd. All rights reserved.2018-06-01T00:00:00ZAverage values of L-functions in even characteristicBae, SunghanJung, Hwanyuphttp://hdl.handle.net/10203/2405842018-03-21T02:20:41Z2018-05-01T00:00:00ZTitle: Average values of L-functions in even characteristic
Authors: Bae, Sunghan; Jung, Hwanyup
Abstract: Let k = F-q(T) be the rational function field over a finite field F-q, where q is a power of 2. In this paper we solve the problem of averaging the quadratic L-functions L(s, chi(u)) over fundamental discriminants. Any separable quadratic extension K of k is of the form K = k(x(u)), where x(u) is a zero of X-2 + X + u = 0 for some u is an element of k. We characterize the family I (resp. F, F') of rational functions u is an element of k such that any separable quadratic extension K of k in which the infinite prime infinity = (1/T) of k ramifies (resp. splits, is inert) can be written as K = k(x(u)) with a unique u is an element of I (resp. u is an element of F, u is an element of F'). For almost all s is an element of C with Re(s) >= 1/2, we obtain the asymptotic formulas for the summation of L(s,chi(u)) over all k(x(u)) with u is an element of I, all k(x(u)) with u is an element of F or all k(x(u)) with u is an element of F' of given genus. As applications, we obtain the asymptotic mean value formulas of L-functions at s = 1/2 and s = 1 and the asymptotic mean value formulas of the class number h(u) or the class number times regulator h(u)R(u). (C) 2017 Elsevier Inc. All rights reserved.2018-05-01T00:00:00ZA sextuple equidistribution arising in Pattern AvoidanceLin, ZhicongKim, Dongsuhttp://hdl.handle.net/10203/2376612018-03-21T01:59:56Z2018-04-01T00:00:00ZTitle: A sextuple equidistribution arising in Pattern Avoidance
Authors: Lin, Zhicong; Kim, Dongsu
Abstract: We construct an intriguing bijection between 021-avoiding inversion sequences and (2413,4213)-avoiding permutations, which proves a sextuple equidistribution involving double Eulerian statistics. Two interesting applications of this result are also presented. Moreover, this result inspires us to characterize all permutation classes that avoid two patterns of length 4 whose descent polynomial equals that of separable permutations.2018-04-01T00:00:00ZRank gain of Jacobian varieties over finite Galois extensionsIm, Bo-HaeWallace, Erikhttp://hdl.handle.net/10203/2371442018-01-30T08:54:59Z2018-03-01T00:00:00ZTitle: Rank gain of Jacobian varieties over finite Galois extensions
Authors: Im, Bo-Hae; Wallace, Erik
Abstract: Let K be a number field, and let X -> P-K(1) be a degree p covering branched only at 0, 1, and infinity. If K is a field containing a primitive p-th root of unity then the covering of P-1 is Galois over K, and if p is congruent to 1 mod 6, then there is an automorphism sigma of X which cyclically permutes the branch points. Under these assumptions, we show that the Jacobian of both X and X/<sigma > gain rank over infinitely many linearly disjoint cyclic degree p-extensions of K. We also show the existence of an infinite family of elliptic curves whose j-invariants are parametrized by a modular function on Gamma(0)(3) and that gain rank over infinitely many cyclic degree 3-extensions of Q.2018-03-01T00:00:00Z