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Showing 1 to 7 of 7 for “"automorphic representation"”.
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Twisted Gan-Gross-Prasad conjecture for unramified quadratic extensions
… groups, and considers the restriction of an automorphic representation of GL(V ) to its subgroup U(V ), for a skew-Hermitian space V. It relates the nonvanishing of a certain period integral to the central value of an L-function attached to the representation. In this thesis, using a relative …
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Level raising for automorphic representations of GL(2n)
… regular algebraic, conjugate self-dual, cuspidal automorphic representation $\Pi$ of $\mathrm{GL}(N)$ over a CM number field $E$ (or, more generally, to a regular algebraic isobaric sum of conjugate self-dual, cuspidal representations), we can attach a continuous $\ell$-adic Galois representation …
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p-adic L-functions of automorphic forms
… a number field, p a prime number. To an (adelic) automorphic representation of GL2 over F (with certain conditions at places above p and ∞) we construct a p-adic L-function which interpolates the complex (Jacquet-Langlands) L-function at the central critical point. This is a generalization of a …
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Eigenvarieties and twisted eigenvarieties
… the case G = GLn, we prove that every self-dual automorphic representation can be deformed into a family of self-dual cuspidal forms containing a Zariski dense subset of classical points. This is the inverse of Ash-Pollack-Stevens conjecture. We also give some hint to this conjecture.
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Self-intersection of Manin-Drinfeld Cycles and Taylor expansion of L-functions
A rising philosophy in the theory of automorphic representations in number theory is that higher central derivatives of L-functions of automorphic forms should correspond to the intersection numbers of special cycles on moduli spaces. A classic early result along this philosophy was achieved by …
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Arithmetic inner product formula for unitary groups
… central derivatives of L-functions of cuspidal automorphic representations for unitary groups of even variables defined over a totally real number field, and their relation with the canonical height of special cycles on Shimura varieties attached to unitary groups of the same size. We formulate …
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Emerton-Gee Stacks, Serre Weights, and Breuil-Mézard Conjectures for GSp_4
… by Gee-Herzig-Savitt for global Galois representations valued in GSp_4 satisfying Taylor--Wiles conditions, and a modularity lifting result for tamely potentially crystalline representations.