DSpace Community: KAIST Dept. of Mathematical Sciences
http://hdl.handle.net/10203/527
KAIST Dept. of Mathematical Sciences2018-06-08T11:47:21ZBounds for the coefficients of cusp forms for Gamma(0)(3)
http://hdl.handle.net/10203/241556
Title: Bounds for the coefficients of cusp forms for Gamma(0)(3)
Authors: Choi, SoYoung; Im, Bo-Hae
Abstract: We give bounds of the coefficients of cusp forms f for Gamma(0)(3) in terms of its first d(k) numbers of coefficients off and f vertical bar W-k(3), where W-3 is the Fricke involution of level 3, and d(k) is the dimension of the space S-k (Gamma(0) (3)) of weight k cusp forms for Gamma(0)(3). In particular, we find bounds of the coefficients of cusp forms for Gamma(+)(0)(3). (C) 2018 Elsevier Inc. All rights reserved.2018-07-01T00:00:00ZSingly periodic free boundary minimal surfaces in a solid cylinder of H-2 x R
http://hdl.handle.net/10203/241401
Title: 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 characteristic
http://hdl.handle.net/10203/240584
Title: 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 new construction of lens spaces
http://hdl.handle.net/10203/242335
Title: A new construction of lens spaces
Authors: Sarkar, Soumen; Suh, Dong Youp
Abstract: Let T-n be the real n-torus group. We introduce a new definition of lens spaces and give some sufficient conditions for diffeomorphic classification of lens spaces. We show that any 3-dimensional lens space L(p; q) is T-2-equivariantly cobordant to zero. We also give some sufficient conditions for higher dimensional lens spaces L(p; q(1), ..., q(n)) to be Tn+1-equivariantly cobordant to zero. General results in equivariant topology imply that torus equivariant complex bordism classes of lens spaces are trivial. In contrast, our proofs are constructive using toric topological arguments. (C) 2018 Elsevier B.V. All rights reserved.2018-05-01T00:00:00Z