Displaying similar documents to “Algebraically constructible functions”

Algebraically constructible chains

Hélène Pennaneac'h (2001)

Annales de l’institut Fourier

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We construct for a real algebraic variety (or more generally for a scheme essentially of finite type over a field of characteristic 0 ) complexes of algebraically and k - algebraically constructible chains. We study their functoriality and compute their homologies for affine and projective spaces. Then we show that the lagrangian algebraically constructible cycles of the cotangent bundle are exactly the characteristic cycles of the algebraically constructible functions.

Reduction of semialgebraic constructible functions

Ludwig Bröcker (2005)

Annales Polonici Mathematici

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Let R be a real closed field with a real valuation v. A ℤ-valued semialgebraic function on Rⁿ is called algebraic if it can be written as the sign of a symmetric bilinear form over R[X₁,. .., Xₙ]. We show that the reduction of such a function with respect to v is again algebraic on the residue field. This implies a corresponding result for limits of algebraic functions in definable families.

A generalisation of an identity of Lehmer

Sanoli Gun, Ekata Saha, Sneh Bala Sinha (2016)

Acta Arithmetica

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We prove an identity involving generalised Euler-Briggs constants, Euler's constant, and linear forms in logarithms of algebraic numbers. This generalises and gives an alternative proof of an identity of Lehmer (1975). Further, this identity facilitates the investigation of the (conjectural) transcendental nature of generalised Euler-Briggs constants. Earlier investigations of similar type by the present authors involved the interplay between additive and multiplicative characters. This...