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A set R⊂N is called rational if it is well approximable by finite unions of arithmetic progressions, meaning that for every \unicode[STIX]x1D716>0 there exists a set B=⋃i=1raiN+bi, where $a_{1},\ldots ,a_ ...
investigate the error term of the asymptotic formula for the number of squarefree integers up to some bound, and lying in some arithmetic progression a (mod q). In particular, we prove an upper bound for its variance as a varies over (Z/qZ)(x) which consid ...
Prof. Laloui gave an interview with RTS about the status of geothermal energy in Switzerland in relation to its progression in other countries. Prof. Laloui discussed how the challenges associated with geothermal energy are primarily technical and how the ...
We explore a few algebraic and geometric structures, through certain questions posed by modern cryptography. We focus on the cases of discrete logarithms in finite fields of small characteristic, the structure of isogeny graphs of ordinary abelian varietie ...
We prove an asymptotic formula for squarefree numbers in arithmetic progressions, improving previous results by Prachar and Hooley. As a consequence we improve a lower bound of Heath-Brown for the least squarefree number in an arithmetic progression. ...
We prove nontrivial bounds for general bilinear forms in hyper-Kloosterman sums when the sizes of both variables may be below the range controlled by Fourier-analytic methods (Polya-Vinogradov range). We then derive applications to the second moment of cus ...
Energy-efficiency is a critical concern for many systems, ranging from Internet of things objects and mobile devices to high-performance computers. Moreover, after 40 years of prosperity, Moore's law is starting to show its economic and technical limits. N ...
This paper presents a framework to derive instantiation-based decision procedures for satisfiability of quantified formulas in first-order theories, including its correctness, implementation, and evaluation. Using this framework we derive decision procedur ...
Numerical software, common in scientific computing or embedded systems, inevitably uses a finite-precision approximation of the real arithmetic in which most algorithms are designed. In many applications, the roundoff errors introduced by finite-precision ...
We show that the exponent of distribution of the ternary divisor function d(3) in arithmetic progressions to prime moduli is at least 1/2 + 1/46, improving results of Friedlander-Iwaniec and Heath-Brown. Furthermore, when averaging over a fixed residue cla ...
