Concept

Euler's totient function

Related publications (12)

Topological Effects in Carbon-based Two-dimensional Nanostructures

Recent advances on low-dimensional and topological materials has greatly inspired the research in condensed matter physics. This thesis is devoted to the computational and theoretical study of topological effects in two-dimensional materials, especially na ...

EPFL2023

Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups

Nicolas Monod

We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring g ...

SPRINGER HEIDELBERG2023

Memoryless Worker-Task Assignment with Polylogarithmic Switching Cost

Adam Teodor Polak

We study the basic problem of assigning memoryless workers to tasks with dynamically changing demands. Given a set of w workers and a multiset T ⊆ [t] of |T| = w tasks, a memoryless worker-task assignment function is any function ϕ that assigns the workers ...

Schloss Dagstuhl -- Leibniz-Zentrum fur Informatik2022

A short note on inadmissible coefficients of weight 2 and 2k+1 newforms

Malik Amir, Andreas Hatziiliou

Let f(z)=q+∑n≥2a(n)qn be a weight k normalized newform with integer coefficients and trivial residual mod 2 Galois representation. We extend the results of Amir and Hong in Amir and Hong (On L-functions of modular elliptic curves and certain K3 surfaces, R ...

2021

A generalization of Kátai's orthogonality criterion with applications

Florian Karl Richter

We study properties of arithmetic sets coming from multiplicative number theory and obtain applications in the theory of uniform distribution and ergodic theory. Our main theorem is a generalization of Kátai's orthogonality cri ...

2019

The second order pullback equation

Bernard Dacorogna, Olivier Kneuss, Gyula Csató

Let f, g be two closed k-forms over R-n. The pullback equation studies the existence of a diffeomorphism phi : R-n -> R-n such that phi*(g) = f. We prove two types of results. The first one sharpens some of the existing regularity results. The second one d ...

Springer2014

What are the Longest Ropes on the Unit Sphere?

Henryk Gerlach

We consider the variational problem of finding the longest closed curves of given minimal thickness on the unit sphere. After establishing the existence of solutions for any given thickness between 0 and 1, we explicitly construct for each given thickness ...

Springer-Verlag2011

Cryptographic Hash Functions in Groups and Provable Properties

Juraj Sarinay

We consider several "provably secure" hash functions that compute simple sums in a well chosen group (G,*). Security properties of such functions provably translate in a natural way to computational problems in G that are simple to define and possibly also ...

EPFL2011

Ideal knots and other packing problems of tubes

Henryk Gerlach

This thesis concerns optimal packing problems of tubes, or thick curves, where thickness is defined as follows. Three points on a closed space curve define a circle. Taking the infimum over all radii of pairwise-distinct point triples defines the thickness ...

EPFL2010

Efficient Protocols for Set Membership and Range Proofs

Rafik Chaabouni

We consider the following problem: Given a commitment to a value σ, prove in zero-knowledge that σ belongs to some discrete set Φ. The set Φ can perhaps be a list of cities or clubs; often Φ can be a numerical range such as [1, 220]. This problem arises in ...

Springer2008

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