Zobrazeno 1 - 10 of 83 pro vyhledávání: '"Hendrik W. Lenstra"'
1
On class groups of random number fields
Autor: Hendrik W. Lenstra, Alex Bartel
Publikováno v: Proceedings of the London Mathematical Society
The main aim of the present paper is to disprove the Cohen--Lenstra--Martinet heuristics in two different ways and to offer possible corrections. We also recast the heuristics in terms of Arakelov class groups, giving an explanation for the probabili
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3a9338b4710de4ae912db8b79f5469fc
https://eprints.gla.ac.uk/177305/7/177305.pdf
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2
Construction of the ring of Witt vectors
Autor: Hendrik W. Lenstra
Publikováno v: European Journal of Mathematics. 5:1234-1241
The paper contains an intelligible construction of the ring W(A) of Witt vectors over an arbitrary commutative ring A.
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::001bf18f21c431781e275ab7efeed607
https://doi.org/10.1007/s40879-018-0294-1
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4
Universal gradings of orders
Autor: Alice Silverberg, Hendrik W. Lenstra
Publikováno v: Lenstra, HW; & Silverberg, A. (2018). Universal gradings of orders. Archiv der Mathematik. doi: 10.1007/s00013-018-1228-3. UC Irvine: Retrieved from: http://www.escholarship.org/uc/item/2dw9s0x2
© 2018, Springer Nature Switzerland AG. For commutative rings, we introduce the notion of a universal grading, which can be viewed as the “largest possible grading”. While not every commutative ring (or order) has a universal grading, we prove t
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a7b4c834c30b2a02eed7d2e885906947
http://www.escholarship.org/uc/item/2dw9s0x2
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5
Commensurability of automorphism groups
Autor: Hendrik W. Lenstra, Alex Bartel
We develop a theory of commensurability of groups, of rings, and of modules. It allows us, in certain cases, to compare sizes of automorphism groups of modules, even when those are infinite. This work is motivated by the Cohen-Lenstra heuristics on c
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ff68d23376ab5ad938f70fb123af2278
https://eprints.gla.ac.uk/149645/7/149645.pdf
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7
Testing isomorphism of lattices over CM-orders
Autor: Hendrik W. Lenstra, Alice Silverberg
A CM-order is a reduced order equipped with an involution that mimics complex conjugation. The Witt-Picard group of such an order is a certain group of ideal classes that is closely related to the "minus part" of the class group. We present a determi
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8
A hyperelliptic smoothness test, II
Autor: Jonathan Pila, Carl Pomerance, Hendrik W. Lenstra
Publikováno v: Proc. London Mathematical Soc., 84(3), 2361-2401
This series of papers presents and rigorously analyzes a probabilistic algorithm for finding small prime factors of an integer. The algorithm uses the Jacobian varieties of curves of genus 2 in the same way that the elliptic curve method uses ellipti
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::16da386ce09b7e947e36bd6d33525061
https://doi.org/10.1112/plms/84.1.105
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9
Explicit Methods in Number Theory
Autor: Don Zagier, Henri Cohen, Hendrik W. Lenstra
Publikováno v: Oberwolfach Reports. :1843-1920
These notes contain extended abstracts on the topic of explicit methods in number theory. The range of topics included modular forms, va- rieties over finite fields, rational and integral points on varieties, class groups, and integer factorization.
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::11eb26f12107014c654fdab1701c9341
https://doi.org/10.4171/owr/2009/33
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10
Algorithms for commutative algebras over the rational numbers
Autor: Alice Silverberg, Hendrik W. Lenstra
Publikováno v: Lenstra, HW; & Silverberg, A. (2018). Algorithms for Commutative Algebras Over the Rational Numbers. Foundations of Computational Mathematics, 18(1), 159-180. doi: 10.1007/s10208-016-9336-6. UC Irvine: Retrieved from: http://www.escholarship.org/uc/item/72w671h6
The algebras considered in this paper are commutative rings of which the additive group is a finite-dimensional vector space over the field of rational numbers. We present deterministic polynomial-time algorithms that, given such an algebra, determin
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