Quantitative distributions of Fourier coefficient relations for twist-inequivalent non-CM newforms yield multiplicity-one refinements and a density criterion for distinguishing newforms.
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4 Pith papers cite this work. Polarity classification is still indexing.
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Constructs equivariant isomorphisms Φ(P,P') between affinized cotangent bundles of Braverman-Kazhdan spaces for conjugate parabolics in SL_n, satisfying Coxeter relations via SL-gauge reflection functors on type A quiver varieties.
Proves unconditional effective joint Sato-Tate distribution for coefficients of two twist-inequivalent non-CM newforms, generalizing to measurable subsets with finite-length curve boundaries and yielding sign-change results for symmetric powers.
A survey paper presents the Geometric Langlands correspondence informally as an algebraic spectral theorem for automorphic sheaves and a blueprint for studying nonabelian symmetry.
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Determining Newforms via various relations among Fourier Coefficients
Quantitative distributions of Fourier coefficient relations for twist-inequivalent non-CM newforms yield multiplicity-one refinements and a density criterion for distinguishing newforms.
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Effective Joint Sato-Tate Distribution and Sign Change of Symmetric Power Coefficients
Proves unconditional effective joint Sato-Tate distribution for coefficients of two twist-inequivalent non-CM newforms, generalizing to measurable subsets with finite-length curve boundaries and yielding sign-change results for symmetric powers.