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Der erste Beitrag von Hans Schneider widmet sich Luthers Reise nach Rom, die dieser noch als Augustinermönch unternommen hat. Kenntnisse über Anlaß, Auftragsgeber, Reiseroute und Verhandlungen in Rom sind bis heute äußerst lückenhaft. Der Verfasser entwickelt auf der Basis neuer Quellen eine These zu Zeitpunkt und Zweck der Reise. Ludwig Uhlig widmet sich im zweiten Beitrag dem noch weitgehend unerforschten anthropologischen Werk von Georg Forster, und zwar anhand einer zoologischen Vorlesung, die er 1786/87 in Wilna gehalten hat. Sie gilt als Forsters gründlichste Arbeit zur Anthropologie. Der Beitrag von Karin Reich wirft neues Licht auf das Verhältnis von Carl Friedrich Gauß zu Leonhard Euler im Zusammenhang eines lange unbekannt gebliebenen Aufsatzes von Euler "Démonstration De la somme de la Suite". Gauß' Abschrift, die lange als verschollen galt, wurde 2009 von Elena Roussanova im Petersburger Archiv der Rußländischen Akademie wiederentdeckt. In der vorliegenden Abhandlung wird sie als Faksimile und in Transkription publiziert und analysiert. In Werner Lehfeldts Beitrag wird auf der Grundlage bisher weitestgehend unbeachtet gebliebener Dokumente die Geschichte von Gauß' Beschäftigung mit der russischen Sprache nachgezeichnet. Es wird deutlich, daß seine zeitweise intensive Beschäftigung mit der russischen Sprache und Literatur eine wichtige Facette der geistigen Physiognomie des "princeps mathematicorum" ausmachen.

Luther, Martin, --- Forster, Georg, --- Euler, Leonhard, --- Gauss, Carl Friedrich, --- Influence --- Europe --- Intellectual life --- Influence. --- Intellectual life. --- Vie intellectuelle --- Euler, Leonhard - Influence. --- Euler, Leonhard, --1707-1783 --Influence. --- Europe - Intellectual life. --- Europe --Intellectual life. --- Forster, Georg - Influence. --- Forster, Georg, --1754-1794 --Influence. --- Gauss, Carl Friedrich - Influence. --- Gauss, Carl Friedrich, --1777-1855 --Influence. --- Luther, Martin - Influence. --- Luther, Martin, --1483-1546 --Influence. --- Kao-ssu, Kʻo-lü-ko, --- Gauss, C. F. --- Gauss, Karl Friedrich, --- Gauss, Carolus Fridericus, --- Gauss, Carlo Federico, --- Forster, Johann Georg Adam, --- Forster, Jerzy, --- Forster, Georgius, --- Forster, George, --- Forster, J. G. --- Fosteris, Georgas, --- Luther, Maarten --- Lutherus, Martinus --- Lutero, Martin --- History & Archaeology --- History - General --- Euler, Leonhard --- Luther, Martin --- Euler, Leonhard. --- Forster, Georg. --- Gauss, Carl Friedrich. --- History of Religion. --- History of Science. --- Luther, Martin. --- HISTORY / General. --- Luther, Martin, - 1483-1546 - Influence --- Forster, Georg, - 1754-1794 - Influence --- Euler, Leonhard, - 1707-1783 - Influence --- Gauss, Carl Friedrich, - 1777-1855 - Influence --- Europe - Intellectual life --- Luter, Martinos, --- Lutr, Martin, --- Лютер, Мартін, --- Li︠u︡ter, Martin, --- Luter, Marcin, --- Luther, Maarten, --- Lutero, Martín, --- Luther, Martinus, --- Luther, Márton, --- Luther, Martti, --- Luther, Martí, --- Lutʻŏ, --- Lūtœ̄, Mātīn, --- D. M. L. A., --- Luters, Mārtiņš, --- Luter, Marṭin, --- Luther, Marczin, --- Rutā, Marutin, --- Joerg, Junker, --- לוטהער, מארטין --- לוטהער, מארטין, --- לותר --- 路德马丁, --- Luttar Cāstiriyār, --- Cāstiriyār, Luttar, --- ルター マルティン, --- Лютэр, Марцін, --- Li︠u︡tėr, Martsin, --- Лутер, Мартин, --- Liuteris, Martynas, --- Lutawm, Matees, --- Lu-toe, Ma-ti, --- Lotera, Martin, --- Lusā, Mātaṅʻ, --- Lūthœ̄, Mātin, --- Luta, Martin, --- Lute̳e̳r, Martẽ, --- Lūthar, Mārṭin, --- Luther, martin (1483-1546) --- Forster, georg (1754-1794) --- Euler, leonhard (1707-1783) --- Gauss, carl friedrich (1777-1855) --- Luther, Martin, - 1483-1546 --- Forster, Georg, - 1754-1794 --- Euler, Leonhard, - 1707-1783 --- Gauss, Carl Friedrich, - 1777-1855

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Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these series and develops their combinatorics. These interesting functions may be described as Whittaker coefficients of Eisenstein series on metaplectic groups, but this characterization doesn't readily lead to an explicit description of the coefficients. The coefficients may be expressed as sums over Kashiwara crystals, which are combinatorial analogs of characters of irreducible representations of Lie groups. For Cartan Type A, there are two distinguished descriptions, and if these are known to be equal, the analytic properties of the Dirichlet series follow. Proving the equality of the two combinatorial definitions of the Weyl group multiple Dirichlet series requires the comparison of two sums of products of Gauss sums over lattice points in polytopes. Through a series of surprising combinatorial reductions, this is accomplished. The book includes expository material about crystals, deformations of the Weyl character formula, and the Yang-Baxter equation.

Dirichlet series. --- Weyl groups. --- Weyl's groups --- Group theory --- Series, Dirichlet --- Series --- BZL pattern. --- Class I. --- Eisenstein series. --- Euler product. --- Gauss sum. --- Gelfand-Tsetlin pattern. --- Kashiwara operator. --- Kashiwara's crystal. --- Knowability Lemma. --- Kostant partition function. --- Riemann zeta function. --- Schur polynomial. --- Schützenberger involution. --- Snake Lemma. --- Statement A. --- Statement B. --- Statement C. --- Statement D. --- Statement E. --- Statement F. --- Statement G. --- Tokuyama's Theorem. --- Weyl character formula. --- Weyl denominator. --- Weyl group multiple Dirichlet series. --- Weyl vector. --- Whittaker coefficient. --- Whittaker function. --- Yang-Baxter equation. --- Yang–Baxter equation. --- accordion. --- adele group. --- affine linear transformation. --- analytic continuation. --- analytic number theory. --- archimedean place. --- basis vector. --- bijection. --- bookkeeping. --- box-circle duality. --- boxing. --- canonical indexings. --- cardinality. --- cartoon. --- circling. --- class. --- combinatorial identity. --- concurrence. --- critical resonance. --- crystal base. --- crystal graph. --- crystal. --- divisibility condition. --- double sum. --- episode. --- equivalence relation. --- f-packet. --- free abelian group. --- functional equation. --- generating function. --- global field. --- ice-type model. --- inclusion-exclusion. --- indexing. --- involution. --- isomorphism. --- knowability. --- maximality. --- nodal signature. --- nonarchimedean local field. --- noncritical resonance. --- nonzero contribution. --- p-adic group. --- p-adic integral. --- p-adic integration. --- partition function. --- polynomial. --- preaccordion. --- prototype. --- reduced root system. --- representation theory. --- residue class field. --- resonance. --- resotope. --- row sums. --- row transfer matrix. --- short pattern. --- six-vertex model. --- snakes. --- statistical mechanics. --- subsignature. --- tableaux. --- type. --- Γ-equivalence class. --- Γ-swap.

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"The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students.The book begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichm©oller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification"--Provided by publisher.

Mappings (Mathematics) --- Class groups (Mathematics) --- Groups, Class (Mathematics) --- Algebraic number theory --- Commutative rings --- Ideals (Algebra) --- Maps (Mathematics) --- Functions --- Functions, Continuous --- Topology --- Transformations (Mathematics) --- 3-manifold theory. --- Alexander method. --- Birman exact sequence. --- BirmanЈilden theorem. --- Dehn twists. --- DehnЌickorish theorem. --- DehnЎielsenЂaer theorem. --- Dennis Johnson. --- Euler class. --- FenchelЎielsen coordinates. --- Gervais presentation. --- Grtzsch's problem. --- Johnson homomorphism. --- Markov partitions. --- Meyer signature cocycle. --- Mod(S). --- Nielsen realization theorem. --- NielsenДhurston classification theorem. --- NielsenДhurston classification. --- Riemann surface. --- Teichmller mapping. --- Teichmller metric. --- Teichmller space. --- Thurston compactification. --- Torelli group. --- Wajnryb presentation. --- algebraic integers. --- algebraic intersection number. --- algebraic relations. --- algebraic structure. --- annulus. --- aspherical manifold. --- bigon criterion. --- braid group. --- branched cover. --- capping homomorphism. --- classifying space. --- closed surface. --- collar lemma. --- compactness criterion. --- complex of curves. --- configuration space. --- conjugacy class. --- coordinates principle. --- cutting homomorphism. --- cyclic subgroup. --- diffeomorphism. --- disk. --- existence theorem. --- extended mapping class group. --- finite index. --- finite subgroup. --- finite-order homeomorphism. --- finite-order mapping class. --- first homology group. --- geodesic laminations. --- geometric classification. --- geometric group theory. --- geometric intersection number. --- geometric operation. --- geometry. --- harmonic maps. --- holomorphic quadratic differential. --- homeomorphism. --- homological criterion. --- homotopy. --- hyperbolic geometry. --- hyperbolic plane. --- hyperbolic structure. --- hyperbolic surface. --- inclusion homomorphism. --- infinity. --- intersection number. --- isotopy. --- lantern relation. --- low-dimensional homology. --- mapping class group. --- mapping torus. --- measured foliation space. --- measured foliations. --- metric geometry. --- moduli space. --- orbifold. --- orbit. --- outer automorphism group. --- pseudo-Anosov homeomorphism. --- punctured disk. --- quasi-isometry. --- quasiconformal map. --- second homology group. --- simple closed curve. --- simplicial complex. --- stretch factors. --- surface bundles. --- surface homeomorphism. --- surface. --- symplectic representation. --- topology. --- torsion. --- torus. --- train track.