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Linear forms in the logarithms of algebraic numbers
1993This chapter is of an auxiliary nature, being mainly concerned with the relationship between bounds for linear forms in the logarithms of algebraic numbers in different (archimedean and non-archimedean) metrics. This material will later be used in the analysis of Thue and Thue-Mahler equations.
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Linear forms, algebraic cycles, and derivatives of L-series
Science China Mathematics, 2019In this paper, the author states some refinements of conjectures due to Gan-Gross-Prasad and Kudla, relating central derivatives of automorphic \(L\)-functions to height pairings of special cycles on Shimura varieties. He also considers analogous conjectures for central values where height pairings are replaced by certain invariant linear forms on ...
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Algebras Generated by Scalar K-atic Forms and Their Linear Forms
Advances in Applied Clifford Algebras, 2006A linear form with an N-elements basis set {e i ; i = 1,...,N} generates an algebra which is that of multivectors, provided some commutation relation is defined to give a meaning to the outer product of the basis vectors. If, moreover, an inner product of sets of K basis vectors is also introduced, for a mapping
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An inequality for a linear form in the logarithms of algebraic numbers
Mathematical Notes of the Academy of Sciences of the USSR, 1969Let ln α1, ..., ln αm−1 be the logarithms of fixed algebraic numbers which are linearly independent over the field of rational numbers, b1, ..., bm−1 rational integers, δ > 0. A bound from below is deduced for the height of the algebraic number αm under the condition that ¦b1 ln α1+...+bm−1ln αm− ¦ < exp {−δH},H=max ¦ b k
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Quadratic Forms, Linear Algebraic Groups, and Cohomology
2010Surveys.- Multiples of forms.- On Saltman's p-Adic Curves Papers.- Serre's Conjecture II: A Survey.- Field Patching, Factorization, and Local-Global Principles.- Deformation Theory and Rational Points on Rationally Connected Varieties.- Recent Progress on the Kato Conjecture.- Elliptic Curves and Iwasawa's = 0 Conjecture.- Cohomological Invariants of ...
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HOMOGENEOUS LINEAR FORMS IN ALGEBRAIC FIELDS
The Quarterly Journal of Mathematics, 1937openaire +1 more source
Weight Hierarchies of a Class of Linear Codes Related to Non-Degenerate Quadratic Forms
IEEE Transactions on Information Theory, 2021Fei Li, Fei Li
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