| 1. |
- Brandes, Julia, et al.
(författare)
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On generating functions in additive number theory, II: lower-order terms and applications to PDEs
- 2021
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Ingår i: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 379, s. 347-76
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Tidskriftsartikel (refereegranskat)abstract
- We obtain asymptotics for sums of the form Sigma(p)(n=1) e(alpha(k) n(k) + alpha(1)n), involving lower order main terms. As an application, we show that for almost all alpha(2) is an element of [0, 1) one has sup(alpha 1 is an element of[0,1)) | Sigma(1 <= n <= P) e(alpha(1)(n(3) + n) + alpha(2)n(3))| << P3/4+epsilon, and that in a suitable sense this is best possible. This allows us to improve bounds for the fractal dimension of solutions to the Schrodinger and Airy equations.
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| 2. |
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Discrete Geometry and Mathematical Morphology : First International Joint Conference, DGMM 2021, Uppsala, Sweden, May 24–27, 2021, Proceedings
- 2021
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Samlingsverk (redaktörskap) (refereegranskat)abstract
- This book constitutes the proceedings of the First IAPR International Conference on Discrete Geometry and Mathematical Morphology, DGMM 2021, which was held during May 24-27, 2021, in Uppsala, Sweden.The conference was created by joining the International Conference on Discrete Geometry for computer Imagery, DGCI, with the International Symposium on Mathematical Morphology, ISMM.The 36 papers included in this volume were carefully reviewed and selected from 59 submissions. They were organized in topical sections as follows: applications in image processing, computer vision, and pattern recognition; discrete and combinatorial topology; discrete geometry - models, transforms, visualization; discrete tomography and inverse problems; hierarchical and graph-based models, analysis and segmentation; learning-based approaches to mathematical morphology; multivariate and PDE-based mathematical morphology, morphological filtering.The book also contains 3 invited keynote papers.
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| 3. |
- Strömberg, Ann-Brith, 1961, et al.
(författare)
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Mixed-Integer Linear Optimization: Primal–Dual Relations and Dual Subgradient and Cutting-Plane Methods
- 2020
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Ingår i: Numerical Nonsmooth Optimization: State of the Art Algorithms. - Cham : Springer International Publishing. ; , s. 499-547, s. 499-547
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- This chapter presents several solution methodologies for mixed-integer linear optimization, stated as mixed-binary optimization problems, by means of Lagrangian duals, subgradient optimization, cutting-planes, and recovery of primal solutions. It covers Lagrangian duality theory for mixed-binary linear optimization, a problem framework for which ultimate success—in most cases—is hard to accomplish, since strong duality cannot be inferred. First, a simple conditional subgradient optimization method for solving the dual problem is presented. Then, we show how ergodic sequences of Lagrangian subproblem solutions can be computed and used to recover mixed-binary primal solutions. We establish that the ergodic sequences accumulate at solutions to a convexified version of the original mixed-binary optimization problem. We also present a cutting-plane approach to the Lagrangian dual, which amounts to solving the convexified problem by Dantzig–Wolfe decomposition, as well as a two-phase method that benefits from the advantages of both subgradient optimization and Dantzig–Wolfe decomposition. Finally, we describe how the Lagrangian dual approach can be used to find near optimal solutions to mixed-binary optimization problems by utilizing the ergodic sequences in a Lagrangian heuristic, to construct a core problem, as well as to guide the branching in a branch-and-bound method. The chapter is concluded with a section comprising notes, references, historical downturns, and reading tips.
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| 4. |
- Gourevitch, D., et al.
(författare)
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EULERIANITY OF FOURIER COEFFICIENTS OF AUTOMORPHIC FORMS
- 2021
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Ingår i: Representation Theory. - : American Mathematical Society (AMS). - 1088-4165. ; 25, s. 481-507
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Tidskriftsartikel (refereegranskat)abstract
- We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another coefficient. We also establish a `hidden' invariance property of Fourier coefficients. We apply these results to minimal and next-to-minimal automorphic representations, and deduce Eulerianity for a large class of Fourier and Fourier-Jacobi coefficients. In particular, we prove Eulerianity for parabolic Fourier coefficients with characters of maximal rank for a class of Eisenstein series in minimal and next-to-minimal representations of groups of ADE-type that are of interest in string theory.
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| 5. |
- Arkeryd, Leif, 1940, et al.
(författare)
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On stationary solutions to normal, coplanar discrete Boltzmann equation models
- 2020
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Ingår i: Communications in Mathematical Sciences. - 1539-6746 .- 1945-0796. ; 18:8, s. 2215-2234
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Tidskriftsartikel (refereegranskat)abstract
- The paper proves existence of renormalized solutions for a class of velocity-discrete coplanar stationary Boltzmann equations with given indata. The proof is based on the construction of a sequence of approximations with L-1- compactness for the integrated collision frequency and gain term. L-1-compactness of a sequence of approximations is obtained using the Kolmogorov-Riesz theorem and replaces the L-1-compactness of velocity averages in the continuous velocity case, not available when the velocities are discrete.
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| 6. |
- Brandes, Julia, 1986
(författare)
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The density of rational lines on hypersurfaces: a bihomogeneous perspective
- 2021
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Ingår i: Monatshefte für Mathematik. - : Springer Science and Business Media LLC. - 1436-5081 .- 0026-9255. ; 195:2, s. 191-231
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Tidskriftsartikel (refereegranskat)abstract
- Let F be a non-singular homogeneous polynomial of degree d in n variables. We give an asymptotic formula of the pairs of integer points (x, y) with | x| ⩽ X and | y| ⩽ Y which generate a line lying in the hypersurface defined by F, provided that n> 2 d-1d4(d+ 1) (d+ 2). In particular, by restricting to Zariski-open subsets we are able to avoid imposing any conditions on the relative sizes of X and Y.
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| 7. |
- Balkanova, O., et al.
(författare)
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NON-VANISHING OF MAASS FORM L-FUNCTIONS AT THE CENTRAL POINT
- 2021
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Ingår i: Proceedings of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9939 .- 1088-6826. ; 149:2, s. 509-523
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider the family {L-j(s)}(j=1)(infinity) of L-functions associated to an orthonormal basis {u(j)}(j=1)(infinity) of even Hecke-Maass forms for the modular group SL(2, Z) with eigenvalues {lambda(j) = kappa(2)(j) + 1/4}(j=1)(infinity). We prove the following effective non-vanishing result: At least 50% of the central values L-j(1/2) with kappa(j) <= T do not vanish as T -> infinity. Furthermore, we establish effective non-vanishing results in short intervals.
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| 8. |
- Mertens, M. H., et al.
(författare)
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Modular forms of virtually real-arithmetic type I: Mixed mock modular forms yield vector-valued modular forms
- 2021
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Ingår i: Mathematical Research Letters. - 1073-2780 .- 1945-001X. ; 28:2, s. 511-561
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Tidskriftsartikel (refereegranskat)abstract
- The theory of elliptic modular forms has gained significant momentum from the discovery of relaxed yet well-behaved notions of modularity, such as mock modular forms, higher order modular forms, and iterated Eichler-Shimura integrals. Applications beyond number theory range from combinatorics, geometry, and representation theory to string theory and conformal field theory. We unify these relaxed notions in the framework of vector-valued modular forms by introducing a new class of SL2(Z)-representations: virtually real-arithmetic types. The key point of the paper is that virtually real-arithmetic types are in general not completely reducible. We obtain a rationality result for Fourier and Taylor coefficients of associated modular forms.
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| 9. |
- Westerholt-Raum, Martin, 1985, et al.
(författare)
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All modular forms of weight 2 can be expressed by Eisenstein series
- 2020
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Ingår i: Research in Number Theory. - : Springer Science and Business Media LLC. - 2522-0160 .- 2363-9555. ; 6:3
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Tidskriftsartikel (refereegranskat)abstract
- We show that every elliptic modular form of integral weight greater than 1 can be expressed as linear combinations of products of at most two cusp expansions of Eisenstein series. This removes the obstruction of nonvanishing central L-values present in all previous work. For weights greater than 2, we refine our result further, showing that linear combinations of products of exactly two cusp expansions of Eisenstein series suffice.
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| 10. |
- Brubaker, B., et al.
(författare)
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Colored five-vertex models and Demazure atoms
- 2021
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Ingår i: Journal of Combinatorial Theory Series A. - : Elsevier BV. - 0097-3165 .- 1096-0899. ; 178
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Tidskriftsartikel (refereegranskat)abstract
- Type A Demazure atoms are pieces of Schur functions, or sets of tableaux whose weights sum to such functions. Inspired by colored vertex models of Borodin and Wheeler, we will construct solvable lattice models whose partition functions are Demazure atoms; the proof of this makes use of a Yang-Baxter equation for a colored five-vertex model. As a byproduct, we will construct Demazure atoms on Kashiwara's B-infinity crystal and give new algorithms for computing Lascoux-Schutzenberger keys. (C) 2020 Elsevier Inc. All rights reserved.
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