Continued fractions have been widely studied in the field of p p -adic numbers alttext="double-struck upper Q Subscript p"> <mml:mr...

The characterization of the gravitational field isolated objects is still an open question in quadratic theories gravity. We study static equilibrium solutions for a self-gravitating fluid extensions General Relativity including terms Weyl tensor $C_{\mu\nu\rho\sigma}$ and Ricci scalar $R$, as suggested by one-loop corrections to classical By means shooting method procedure we link total mass s...

Let k be a field of characteristic different from 2. Let E/k be a finite separable extension with a k-linear involution σ. For every σ-symmetric element μ ∈ E∗, we define a hermitian scaled trace form by x ∈ E 7→ TrE/k(μxx). If μ = 1, it is called a hermitian trace form. In the following, we show that every even-dimensional quadratic form over a hilbertian field, which is not isomorphic to the ...

We describe a modification to the well-known large prime variant of the multiple polynomial quadratic sieve factoring algorithm. In practice this leads to a speed-up factor of 2 to 2.5. We discuss several implementation-related aspects, and we include some examples. Our new variation is also of practical importance for the number field sieve factoring algorithm. 1. Factoring with two large prim...

This is the introductory chapter to this issue. We review the main idea of the localization technique and its brief history both in geometry and in QFT. We discuss localization in diverse dimensions and give an overview of the major applications of the localization calculations for supersymmetric theories. We explain the focus of the present issue.

We describe an enhanced version of the TWINKLE factoring device and analyse to what extent it can be expected to speed up the sieving step of the Quadratic Sieve and Number Field Sieve factoring algorithms. The bottom line of our analysis is that the TWINKLE-assisted factorization of 768-bit numbers is difficult but doable in about 9 months (including the sieving and matrix parts) by a large or...

In this note we study an analogy between a positive definite quadratic form for elliptic curves over finite fields and a positive definite quadratic form for elliptic curves over the rational number field. A question is posed of which an affirmative answer would imply the analogue of the Riemann hypothesis for elliptic curves over the rational number field.

While the unit group of an imaginary quadratic field is very simple, the unit group of a real quadratic field has nontrivial structure. Its study involves some geometry and analysis, but also it relates to Pell's equation and continued fractions, topics from elementary number theory.