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Concept

Suite arithmétique

Publications associées (17)

Rankin-Selberg coefficients in large arithmetic progressions

Philippe Michel, Yongxiao Lin

Let (?(f) (n))(n=1) be the Hecke eigenvalues of either a holomorphic Hecke eigencuspform or a Hecke-Maass cusp form f. We prove that, for any fixed ? > 0, under the Ramanujan-Petersson conjecture for GL(2) Maass forms, the Rankin-Selberg coefficients (?(f) ...

SCIENCE PRESS2023

Arithmetic and geometric deformations of threefolds

Stefano Filipazzi, Fabio Bernasconi

We show that mixed-characteristic and equicharacteristic small deformations of 3-dimensional canonical (resp., terminal) singularities with perfect residue field of characteristic p>5 are canonical (resp., terminal). We discuss applications to arithmetic a ...

Wiley2023

Equivalent black carbon concentration in 10 minutes time resolution, measured in the Swiss container during MOSAiC 2019/2020

Julia Schmale, Ivo Fabio Beck, Lubna Dada, Benjamin Jérémy Laurent Heutte

This dataset contains equivalent black carbon (eBC) concentrations, averaged to 10 min time resolution, measured during the year-long MOSAiC expedition from October 2019 to September 2020. The measurements were performed in the Swiss container on the D-dec ...

Zenodo2022

Rethinking protein aggregation and drug discovery in neurodegenerative diseases: Why we need to embrace complexity?

Hilal Lashuel

More than a century has passed since pathological protein aggregates were first identified in the brains of patients with neurodegenerative diseases (NDDs). Yet, we still do not have effective therapies to treat or slow the progression of these devastating ...

2021

On arithmetic progressions in symmetric sets in finite field model

Jan Hazla

We consider two problems regarding arithmetic progressions in symmetric sets in the finite field (product space) model. ...

ELECTRONIC JOURNAL OF COMBINATORICS2020

On the distribution of squarefree integers in arithmetic progressions

Pierre Francis André Le Boudec

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 ...

SPRINGER HEIDELBERG2018

Arithmetic and geometric structures in cryptography

Benjamin Pierre Charles Wesolowski

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 ...

EPFL2018

On The Least Squarefree Number In An Arithmetic Progression

Ramon Moreira Nunes

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. ...

London Math Soc2017

Bilinear forms with Kloosterman sums and applications

Philippe Michel

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 ...

Annal Mathematics2017

Design and Applications of Approximate Circuits by Gate-Level Pruning

Christian Enz, Vincent Frédéric Camus, Jérémy Lucien Maurice Schlachter

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 ...

Ieee-Inst Electrical Electronics Engineers Inc2017

Solving quantified linear arithmetic by counterexample-guided instantiation

Viktor Kuncak, Andrew Joseph Reynolds

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 ...

2017

On The Exponent Of Distribution Of The Ternary Divisor Function

Philippe Michel

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 ...

London Mathematical Society, Cambridge2015

Computation Over Gaussian Networks With Orthogonal Components

Michael Christoph Gastpar, Chien-Yi Wang

Function computation over Gaussian networks with orthogonal components is studied for arbitrarily correlated discrete memoryless sources. Two classes of functions are considered: 1) the arithmetic sum function and 2) the type function. The arithmetic sum f ...

Institute of Electrical and Electronics Engineers2014

Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions

Philippe Michel

We show that, in a restricted range, the divisor function of integers in residue classes modulo a prime follows a Gaussian distribution, and a similar result for Hecke eigenvalues of classical holomorphic cusp forms. Furthermore, we obtain the joint distri ...

European Mathematical Soc2014

Computation over Gaussian networks with orthogonal components

Michael Christoph Gastpar, Chien-Yi Wang

Function computation of arbitrarily correlated discrete sources over Gaussian networks with multiple access components but no broadcast is studied. Two classes of functions are considered: the arithmetic sum function and the frequency histogram function. T ...

2013

Synthesis of Fixed-Point Programs

Viktor Kuncak, Eva Darulova

Several problems in the implementations of control systems, signal-processing systems, and scientific computing systems reduce to compiling a polynomial expression over the reals into an imperative program using fixed-point arithmetic. Fixed-point arithmet ...

2013

Data-flow transformations to maximize the use of carry-save representation in arithmetic circuits

Paolo Ienne, Philip Brisk, Ajay Kumar Verma

The increasing importance,of datapath circuits in complex systems-on-chip calls for special arithmetic optimizations. The goal is to automatically achieve the handcrafted results which escape classic logic optimizations. Some work has been done in the rece ...

2008