K3 surfaces, cyclotomic polynomials and orthogonal groups
Graph Chatbot
Chat with Graph Search
Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.
DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.
We consider the problem of sampling at unknown locations. We prove that, in this setting, if we take arbitrarily many samples of a polynomial or real bandlimited signal, it is possible to find another function in the same class, arbitrarily far away from t ...
For~q a prime power, the discrete logarithm problem (DLP) in~\Fq consists in finding, for any g∈Fq× and h∈⟨g⟩, an integer~x such that gx=h. We present an algorithm for computing discrete logarithm ...
Formal verification utilizing symbolic computer algebra has demonstrated the ability to formally verify large Galois field arithmetic circuits and basic architectures of integer arithmetic circuits. The technique models the circuit as Gröbner basis polynom ...
For q a prime power, the discrete logarithm problem (DLP) in Fq consists in finding, for any g∈Fq× and h∈⟨g⟩, an integer x such that gx=h. We present an algorithm for computing discrete log ...
Let k be a global field of characteristic not 2, and let f is an element of k[X] be an irreducible polynomial. We show that a non-degenerate quadratic space has an isometry with minimal polynomial f if and only if such an isometry exists over all the compl ...
We present novel Markov-type and Nikolskii-type inequalities for multivariate polynomials associated with arbitrary downward closed multi-index sets in any dimension. Moreover, we show how the constant of these inequalities changes, when the polynomial is ...
In this paper we give a new proof of the ELSV formula. First, we refine an argument of Okounkov and Pandharipande in order to prove (quasi-)polynomiality of Hurwitz numbers without using the ELSV formula (the only way to do that before used the ELSV formul ...
Let k be an algebraically closed field. Let P(X-11,...,X-nn, T) be the characteristic polynomial of the generic matrix (X-ij) over k. We determine its singular locus as well as the singular locus of its Galois splitting. If X is a smooth quasi-projective s ...
The Uniformization Theorem due to Koebe and Poincaré implies that every compact Riemann surface of genus greater or equal to 2 can be endowed with a metric of constant curvature – 1. On the other hand, a compact Riemann surface is a complex algebraic curve ...
This work contains the study of the algebra called al-Badī‘ fī al-ḥisāb (literally : "the Wonderful on calculation"), written by the Persian mathematician Abu Bakr Muḥammad ibn al-Ḥusain al-Karaǧi (previously known as ...