Topic
Divisor
About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.
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TL;DR: The floor and the ceiling of a divisor supported by collinear places of the Hermitian function field are determined and are found to give new bounds for the minimum distance of algebraic geometry codes.
16 citations
TL;DR: In this paper, an explicit slice of Givental's Lagrangian cone for Gromov-Witten theory of the root stack was constructed for a smooth projective variety X with a smooth divisor D and a positive integer r.
Abstract: Given a smooth projective variety X with a smooth nef divisor D and a positive integer r, we construct an I-function, an explicit slice of Givental’s Lagrangian cone, for Gromov–Witten theory of the root stack $$X_{D,r}$$
. As an application, we also obtain an I-function for relative Gromov–Witten theory following the relation between relative and orbifold Gromov–Witten invariants.
16 citations
TL;DR: The main theme of as mentioned in this paper is to systematize the Hardy-Landau and Hardy-Omega results on the divisor problem and the circle problem, and the results of Richert and later modifications by Warlimont.
Abstract: The main theme of this paper is to systematize the Hardy-Landau $\Omega$ results and the Hardy $\Omega_{\pm}$ results on the divisor problem and the circle problem. The method of ours is general enough to include the abelian group problem and the results of Richert and the later modifications by Warlimont, and in fact theorem 6 of ours is an improvement of their results. All our results are effective as in our earlier paper II with the same title. Some of our results are new.
16 citations
TL;DR: In this article, generalizations of generic vanishing theorems to a ℚ -divisor setting can be used to study the geometric properties of pluritheta divisors on a principally polarized Abelian variety.
Abstract: The purpose of this paper is to show how generalizations of generic vanishing theorems to a ℚ -divisor setting can be used to study the geometric properties of pluritheta divisors on a principally polarized Abelian variety (PPAV for short).
16 citations
01 Apr 1995
TL;DR: In this article, an improved method for expressing the greatest common divisor of n numbers as an integer linear combination of the numbers is presented and analyzed, both theoretically and practically, both in the light of the current knowledge about the complexity of extended gcd computations.
Abstract: An improved method for expressing the greatest common divisor of n numbers as an integer linear combination of the numbers is presented and analyzed, both theoretically and practically. The performance of this algorithm is compared with other methods, indicating substantial improvements in the size of the solution. The results are given in the light of the current knowledge about the complexity of extended gcd computations. Thus, finding optimal sets of multipliers has been proved to be an NP-complet e problem, We present a relatively efficient approximation algorithm with excellent performance. This problem is interesting in its own right. Furthermore, it has important applications, for example in computing canonical normal forms of integer matrices.
16 citations