منابع مشابه
Bounds for Modular L-functions in the Level Aspect
Let f be a primitive (holomorphic or Maaß) cusp form of level q and nontrivial nebentypus. Then for Re s = 1 2 the associated L-function satisfies L(f, s) q 1 4 − 1 1889 , where the implied constant depends polynomially on s and the archimedean parameters of f (weight or Laplacian eigenvalue). Résumé. Soit f une forme modulaire cuspidale primitive (holomorphe ou de Maaß) de niveau q et de carac...
متن کاملImproved Bounds for Reduction to Depth 4 and Depth 3
Koiran [8] showed that if an n-variate polynomial fn of degree d (with d = n) is computed by a circuit of size s, then it is also computed by a homogeneous circuit of depth four and of size 2 √ d log(n) . Using this result, Gupta, Kamath, Kayal and Saptharishi [7] found an upper bound for the size of a depth three circuit computing fn. We improve here Koiran’s bound. Indeed, we show that it is ...
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We answer positively a question of Asia Rauf for the case of intersections of three prime ideals generated by disjoint sets of variables and we present several inequalities on Stanley depth. This is a detailed presentation of our talk at the conference on ”Fundamental structures of algebra” in honor of Prof. Serban Basarab at his 70-th anniversary. Let S = K[x1, . . . , xn] be a polynomial alge...
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We show that the minimum size of a depth-two N-superconcentrator is (N log 2 N= loglog N). Before this work, optimal bounds were known for all depths except two. For the upper bound, we build superconcentrators by putting together a small number of disperser graphs; these disperser graphs are obtained using a probabilistic argument. We present two diierent methods for showing lower bounds. Firs...
متن کاملComputational Lower Bounds for Colourful Simplicial Depth
The colourful simplicial depth problem in dimension d is to find a configuration of (d+1) sets of (d+1) points such that the origin is contained in the convex hull of each set (colour) but contained in a minimal number of colourful simplices generated by taking one point from each set. A construction attaining d + 1 simplices is known, and is conjectured to be minimal. This has been confirmed u...
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ژورنال
عنوان ژورنال: Forum Mathematicum
سال: 2019
ISSN: 1435-5337,0933-7741
DOI: 10.1515/forum-2018-0080