You have just completed your registration at OpenAire.
Before you can login to the site, you will need to activate your account.
An e-mail will be sent to you with the proper instructions.
Important!
Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version
of the site upon release.
International audience; Let k be a quadratic field. We give an explicit formula for the Dirichlet series enumerating cubic fields whose quadratic resolvent field is isomorphic to k. Our work is a sequel to previous work of Cohen and Morra, where such formulas are proved in a more general setting, in terms of sums over characters of certain groups related to ray class groups. In the present paper we carry the analysis further and prove explicit formulas for these Dirichlet series over Q. In a ...
22 pages, some improvements and corrections, especially in Sections 4 and 5.; We describe an algorithm that allows to compute the Euclidean minimum (for the norm form) of any order of a totally definite quaternion field over a number field K of degree strictly greater than 1. Our approach is a generalization of previous work dealing with number fields. The algorithm was practically implemented when K has degree 2.
The main step in numerical evaluation of classical Sl2 (Z) modular forms and elliptic functions is to compute the sum of the first N nonzero terms in the sparse q-series belonging to the Dedekind eta function or the Jacobi theta constants. We construct short addition sequences to perform this task using N + o(N) multiplications. Our constructions rely on the representability of specific quadratic progressions of integers as sums of smaller numbers of the same kind. For example, we show that e...
International audience; We describe a new implementation of the elementary transcendental functions exp, sin, cos, log and atan for variable precision up to approximately 4096 bits. Compared to the MPFR library, we achieve a maximum speedup ranging from a factor 3 for cos to 30 for atan. Our implementation uses table-based argument reduction together with rectangular splitting to evaluate Taylor series. We collect denominators to reduce the number of divisions in the Taylor series, and avoid ...
We describe an efficient algorithm for the computation of separable isogenies between abelian varieties represented in the coordinate system given by algebraic theta functions. Let $A$ be an abelian variety of dimension $g$ defined over a field of odd characteristic. Our algorithm decomposes in two principal steps. First, given a theta null point for $A$ and a subgroup $K$ isotropic for the Weil pairing, we explain how to compute the theta null point corresponding to the quotient abelian vari...
16 pages; International audience; Assuming the Generalized Riemann Hypothesis, Bach has shown that one can calculate the residue of the Dedekind zeta function of a number field K by a clever use of the splitting of primes p < X, with an error asymptotically bounded by 8.33 log D_K/(\sqrt{X}\log X), where D_K is the absolute value of the discriminant of K. Guided by Weil's explicit formula and still assuming GRH, we make a different use of the splitting of primes and thereby improve Bach's con...
International audience; We determine the conditions under which singular values of multiple $\eta$-quotients of square-free level, not necessarily prime to~$6$, yield class invariants, that is, algebraic numbers in ring class fields of imaginary-quadratic number fields. We show that the singular values lie in subfields of the ring class fields of index $2^{k' - 1}$ when $k' \geq 2$ primes dividing the level are ramified in the imaginary-quadratic field, which leads to faster computations of e...
No project research data found
No project statistics found
Scientific Results
Chart is loading... It may take a bit of time. Please be patient and don't reload the page.
PUBLICATIONS BY ACCESS MODE
Chart is loading... It may take a bit of time. Please be patient and don't reload the page.
Publications in Repositories
Chart is loading... It may take a bit of time. Please be patient and don't reload the page.