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Feasibility of primality in bounded arithmetic
Forum of Mathematics, SigmaWe prove the correctness of the AKS algorithm [1] within the bounded arithmetic theory $T^{\text {count}}_2$ or, equivalently, the first-order consequences of the theory $\text {VTC}^0$ expanded by the smash function, which we denote by
Raheleh Jalali, Ondřej Ježil
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The Mean Square of the Hurwitz Zeta-Function in Short Intervals
AxiomsThe Hurwitz zeta-function ζ(s,α), s=σ+it, with parameter ...
Antanas Laurinčikas +1 more
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A Relative Bigness Inequality and Equidistribution Theorem over Function Fields [PDF]
International Journal of Number Theory, 2021 For any line bundle written as a subtraction of two ample line bundles, Siu's inequality gives a criterion on its bigness. We generalize this inequality to a relative case.
Wen-wei Luo
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Stronger arithmetic equivalence
Discrete Analysis, 2021 Stronger arithmetic equivalence, Discrete Analysis 2021:23, 23 pp. An algebraic number field is a subfield $K$ of $\mathbb C$ that is finite-dimensional when considered as a vector space over $\mathbb Q$, which implies that every element of $K$ is ...
Andrew V. Sutherland
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Torsion Limits and Riemann-Roch Systems for Function Fields and Applications [PDF]
IEEE Transactions on Information Theory, 2012 The Ihara limit (or constant) A(q) has been a central problem of study in the asymptotic theory of global function fields (or equivalently, algebraic curves over finite fields).
Ignacio Cascudo, R. Cramer, C. Xing
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Quadratic forms and linear algebraic groups [PDF]
, 2009 Topics discussed at the workshop Quadratic Forms and Linear Algebraic Groups included besides the algebraic theory of quadratic and Hermitian forms and their Witt groups several aspects of the theory of linear algebraic groups and homogeneous varieties ...
Harbater, David +2 more
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Ray class fields of global function fields with many rational places [PDF]
, 1998 0. Introduction. Algebraic curves over finite fields with many rational points have been of increasing interest in the last two decades. The question of explicitly determining the maximal number of points on a curve of given genus was initiated and in ...
Roland Auer
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The arithmetic Hodge index theorem and rigidity of dynamical systems over function fields
Pacific Journal of Mathematics, 2018 In one of the fundamental results of Arakelov's arithmetic intersection theory, Faltings and Hriljac (independently) proved the Hodge Index Theorem for arithmetic surfaces by relating the intersection pairing to the negative of the N\'eron-Tate height ...
Alexander Carney
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Complex Multiplication Symmetry of Black Hole Attractors [PDF]
, 2003 We show how Moore's observation, in the context of toroidal compactifications in type IIB string theory, concerning the complex multiplication structure of black hole attractor varieties, can be generalized to Calabi-Yau compactifications with finite ...
Andrianopoli +49 more
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A Kronecker limit formula for totally real fields and arithmetic applications
Research in Number Theory, 2015 We establish a Kronecker limit formula for the zeta function ζF(s,A) of a wide ideal class A of a totally real number field F of degree n. This formula relates the constant term in the Laurent expansion of ζF(s,A) at s=1 to a toric integral of a SLn(ℤ ...
Sheng-chi Liu, R. Masri
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