Modular forms and three-manifold invariants
Exceptional zeros and L invariants of Bianchi modular forms
... the modular curve has no complex or algebraic structure, making it much harder to attach Galois representations to automorphic ...of modular forms, which also plays a prominent role in the proof of ...
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Modern aspects of topological gauge theories Polynomial invariants and mock modular forms
... These theories were to shape not only the physics of the previous and future centuries but also they played a fundamental role to the enormous technological revolution that is still ongoing. These two newly established ...
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Invariants of binary forms
... binary forms of arbitrary order n, but we would have to have some things into ...for forms of order greater or equal to 3, as the first step of the algorithm is to pick three of the roots of the ...
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SIEGEL MODULAR FORMS OF DEGREE THREE AND THE COHOMOLOGY OF LOCAL SYSTEMS
... Siegel modular forms of a certain type; the remaining terms admit a surprisingly simple description in terms of the motivic Euler characteristics for lower ...genus three and abelian threefolds over ...
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DEGREE THREE COHOMOLOGICAL INVARIANTS OF SEMISIMPLE GROUPS
... ∆ is the decomposition group of T gen . Moreover, ch is an isomorphism, hence the restriction homomorphism R(G) → R(T gen ) = Z[Λ] ∆ is an isomorphism for a quasi-split G. 3b. Root systems and invariant quadratic ...
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Class invariants from a new kind of Weber like modular equation
... to forms in classes from distinct cosets of H ...quotients. Modular equations involving generalisations of the Weber functions have been investigated for this purpose [10], and whilst leading to interesting ...
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Topological invariants of knots: three routes to the Alexander Polynomial
... So far we have constructed our knots explicitly, but knots also arise naturally in other situations such as the closure of braids or random walks or, importantly for this chapter, the boundaries of surfaces. Here, we ...
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Contributions to the theory of modular forms and L-functions
... The class number turns out to be one of the most important invariants of a number field. Although a lot of effort has been put into finding relations to other mathematical areas (such as L-functions, cotangent ...
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Images of adelic Galois representations for modular forms
... a modular eigenform f, then one has p-adic Galois representations ρ f,p and an adelic representation ρ f , and it is natural to ask whether analogues of theorems (A)–(C) hold in this ...For modular ...
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Dimension Formulae for Spaces of Lifted Bianchi Modular Forms
... In what follows, we will assume for simplicity that 2 is unramified in K. We treat first the case n = 1, and then in the following three sections we treat the case n = 2, one type at a time. We then finish with ...
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Weight Reduction for Mod l Bianchi Modular Forms
... H 0 (Γ, I r,s ) ∼ = n F ℓ (ℓ − 1) if r ≡ s ≡ 0 (mod ℓ − 1) 0 otherwise Proof. By Shapiro’s Lemma, we have H 0 (Γ, I r,s ) ≃ H 0 (Γ 0 (ℓ), (F ℓ ) χ(r,s) ). In action of Γ 0 (ℓ) on F ell through χ(r, s), either there are ...
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CiteSeerX — Milnor Link Invariants And Quantum 3-Manifold Invariants
... Milnor invariants of high order, will live in high degree in the corresponding algebra of Feyn- man ...Milnor's invariants of links and proven in a separate ...
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Invariants of binary forms
... two forms included in the irredu- cible system as derived by the methods of Gordan and Clebsch were found to be ...binary forms up to the octavic may be considered as accurately determined by the two ...
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Finite groups, spherical 2-categories, and 4-manifold invariants
... Brown has computed some homotopy 3-types using the theory of crossed N- cubes of groups. Hopefully his results will provide more concrete examples of our construction. We can ask ourselves how powerful we can expect our ...
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Finding Exact Forms on a Thermodynamic Manifold
... 2D manifold. Of particular interest are the exact 1-forms on the cotangent space of that manifold, since the integral of exact 1-forms is path-independent, a crucial property satisfied by ...
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Spaces of modular forms. Modular curves and dimensions
... Before Wiles, (FLT) ` had been proved for all primes ` less than four million. Taniyama–Shimura conjecture On the other hand, in the middle of the 20th century, the Japanese mathe- maticians Yutaka Taniyama and Goro ...
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MAASS FORMS, MODULAR FORMS, AND REPRESENTATION THEORY
... The theory of root systems already shows from this that the raising and lowering operators are supposed to go between the weight spaces of weights differing by 2 without killing anything[r] ...
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State sum invariants of three manifolds
... Newman-Gomez, Sharon Angela, "State sum invariants of three manifolds" (1998). Theses Digitization Project. 1510. https://scholarworks.lib.csusb.edu/etd-project/1510 This Project is brought to you for free ...
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Elliptic Modular Forms and Their Applications
... of modular forms of a given weight on Γ is finite dimen- sional and algorithmically computable, so that it is a mechanical procedure to prove any given identity among modular ...Secondly, ...
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On the critical points of modular forms
... each modular form, an equivariant function that commutes with the action of the modular ...every modular forms has infinitely many inequivalent zeros in the upper ...quasimodular forms ...
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