Affine congruences and rational points on a certain cubic surface

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Some consequences of Masser's counting theorem on elliptic curves

Valéry Aurélien Mahé

We use Masser's counting theorem to prove a lower bound for the canonical height in powers of elliptic curves. We also prove the Galois case of the elliptic Lehmer problem, combining Kummer theory and Masser's result with bounds on the rank and torsion of ...

Springer Heidelberg2017

The effect of overall stimulus configuration on crowding

Michael Herzog, Maya Roinishvili, Mattew Pachai

The standard framework to study vision is typically hierarchical and feedforward, which facilitates deconstructing complex mechanisms into smaller, more tractable problems. However, this framework can fail when elements are presented in context, as they ar ...

2017

Tunable insertion of multiple lines into a Kerr frequency comb using electro-optical modulators

Tobias Kippenberg, Maxim Karpov, Martin Hubert Peter Pfeiffer, Arne Kordts, Yan Yan, Lin Zhang, Ahmad Fallahpour, Amirhossein Mohajerin Ariaei, Cong Liu

We experimentally insert a flexible number of electro-optical (EO) comb lines into a Kerr frequency comb via EO modulation and demonstrate the use of combined Kerr and EO combs as light sources in coherent communications. The number of EO lines inserted in ...

Optical Society of America2017

Inhomogeneous minima of mixed signature lattices

Eva Bayer Fluckiger, Martino Borello, Peter Simon Jossen

We establish an explicit upper bound for the Euclidean minimum of a number field which depends, in a precise manner, only on its discriminant and the number of real and complex embeddings. Such bounds were shown to exist by Davenport and Swinnerton-Dyer ([ ...

Academic Press Inc Elsevier Science2016

Motivic Classes of Nakajima Quiver Varieties

Dimitri Stelio Wyss

We prove that Hausel’s formula for the number of rational points of a Nakajima quiver variety over a finite field also holds in a suitable localization of the Grothendieck ring of varieties. In order to generalize the arithmetic harmonic analysis in his pr ...

2016

Independence number of generalized Petersen graphs

Javad Ebrahimi Boroojeni

Determining the size of a maximum independent set of a graph G, denoted by alpha(G), is an NP-hard problem. Therefore many attempts are made to find upper and lower bounds, or exact values of alpha(G) for special classes of graphs. This paper is aimed towa ...

Charles Babbage Res Ctr2016

Height of rational points on quadratic twists of a given elliptic curve

Pierre Francis André Le Boudec

We formulate a conjecture about the distribution of the canonical height of the lowest non-torsion rational point on a quadratic twist of a given elliptic curve, as the twist varies. This conjecture seems to be very deep and we can prove only partial resul ...

Oxford Univ Press2016

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