On Dwork's $p$-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On Dwork's $p$-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps write by E. Delaygue. This book was released on 2017-02-20. On Dwork's $p$-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps available in PDF, EPUB and Kindle. Using Dwork's theory, the authors prove a broad generalization of his famous -adic formal congruences theorem. This enables them to prove certain -adic congruences for the generalized hypergeometric series with rational parameters; in particular, they hold for any prime number and not only for almost all primes. Furthermore, using Christol's functions, the authors provide an explicit formula for the “Eisenstein constant” of any hypergeometric series with rational parameters. As an application of these results, the authors obtain an arithmetic statement “on average” of a new type concerning the integrality of Taylor coefficients of the associated mirror maps. It contains all the similar univariate integrality results in the literature, with the exception of certain refinements that hold only in very particular cases.
2017 MATRIX Annals
2017 MATRIX Annals - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook 2017 MATRIX Annals write by Jan de Gier. This book was released on 2019-03-13. 2017 MATRIX Annals available in PDF, EPUB and Kindle. MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the eight programs held at MATRIX in its second year, 2017: - Hypergeometric Motives and Calabi–Yau Differential Equations - Computational Inverse Problems - Integrability in Low-Dimensional Quantum Systems - Elliptic Partial Differential Equations of Second Order: Celebrating 40 Years of Gilbarg and Trudinger’s Book - Combinatorics, Statistical Mechanics, and Conformal Field Theory - Mathematics of Risk - Tutte Centenary Retreat - Geometric R-Matrices: from Geometry to Probability The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.
Special Values of the Hypergeometric Series
Special Values of the Hypergeometric Series - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Special Values of the Hypergeometric Series write by Akihito Ebisu. This book was released on 2017-07-13. Special Values of the Hypergeometric Series available in PDF, EPUB and Kindle. In this paper, the author presents a new method for finding identities for hypergeoemtric series, such as the (Gauss) hypergeometric series, the generalized hypergeometric series and the Appell-Lauricella hypergeometric series. Furthermore, using this method, the author gets identities for the hypergeometric series and shows that values of at some points can be expressed in terms of gamma functions, together with certain elementary functions. The author tabulates the values of that can be obtained with this method and finds that this set includes almost all previously known values and many previously unknown values.
Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem
Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem write by Denis R. Hirschfeldt. This book was released on 2017-09-25. Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem available in PDF, EPUB and Kindle. Goncharov and Peretyat'kin independently gave necessary and sufficient conditions for when a set of types of a complete theory is the type spectrum of some homogeneous model of . Their result can be stated as a principle of second order arithmetic, which is called the Homogeneous Model Theorem (HMT), and analyzed from the points of view of computability theory and reverse mathematics. Previous computability theoretic results by Lange suggested a close connection between HMT and the Atomic Model Theorem (AMT), which states that every complete atomic theory has an atomic model. The authors show that HMT and AMT are indeed equivalent in the sense of reverse mathematics, as well as in a strong computability theoretic sense and do the same for an analogous result of Peretyat'kin giving necessary and sufficient conditions for when a set of types is the type spectrum of some model.
Knot Invariants and Higher Representation Theory
Knot Invariants and Higher Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Knot Invariants and Higher Representation Theory write by Ben Webster. This book was released on 2018-01-16. Knot Invariants and Higher Representation Theory available in PDF, EPUB and Kindle. The author constructs knot invariants categorifying the quantum knot variants for all representations of quantum groups. He shows that these invariants coincide with previous invariants defined by Khovanov for sl and sl and by Mazorchuk-Stroppel and Sussan for sl . The author's technique is to study 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations. These are the representation categories of certain finite dimensional algebras with an explicit diagrammatic presentation, generalizing the cyclotomic quotient of the KLR algebra. When the Lie algebra under consideration is sl , the author shows that these categories agree with certain subcategories of parabolic category for gl .
