Conjugation of elements in central simple algebras

Villa, Oliver

doi:10.1080/00927872.2016.1233188

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Averages Of Representation Numbers1

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2016

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“…Remark. One could also use recent results of Villa [28] for the proof of the above theorem. Then there is a bijective correspondence between (unordered) pairs of embeddings ϕ 1 , ϕ 2 : k → D K with ϕ 2 (x) = ϕ 1 (x) for all x ∈ k and binary quadratic subspaces W of determinant d of V .…”

Section: Averages Of Representation Numbersmentioning

confidence: 99%

Averages of Fourier coefficients of Siegel modular forms and representation of binary quadratic forms by quadratic forms in four variables

Schulze-Pillot

2016

Math. Ann.

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Let −d be a a negative discriminant and let T vary over a set of representatives of the integral equivalence classes of integral binary quadratic forms of discriminant −d. We prove an asymptotic formula for d → ∞ for the average over T of the number of representations of T by an integral positive definite quaternary quadratic form and obtain bounds for averages of Fourier coefficients of linear combinations of Siegel theta series. We also find an asymptotic estimate from below on the number of binary forms of fixed discriminant −d which are represented by a given quaternary form. In particular, we can show that for growing d a positive proportion of the binary quadratic forms of discriminant −d is represented by the given quaternary quadratic form.

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Section: Averages Of Representation Numbersmentioning

confidence: 99%

Averages of Fourier coefficients of Siegel modular forms and representation of binary quadratic forms by quadratic forms in four variables

Schulze-Pillot

2016

Math. Ann.

View full text Add to dashboard Cite

show abstract

Conjugation of elements in central simple algebras

Cited by 1 publication

References 3 publications

Averages of Fourier coefficients of Siegel modular forms and representation of binary quadratic forms by quadratic forms in four variables

Averages of Fourier coefficients of Siegel modular forms and representation of binary quadratic forms by quadratic forms in four variables

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