Concept

Hypothèse de Riemann généralisée

Publications associées (22)

When do Minimax-fair Learning and Empirical Risk Minimization Coincide?

Minimax-fair machine learning minimizes the error for the worst-off group. However, empirical evidence suggests that when sophisticated models are trained with standard empirical risk minimization (ERM), they often have the same performance on the worst-of ...

2023

On the Use of the Generalized Littlewood Theorem Concerning Integrals of the Logarithm of Analytical Functions for the Calculation of Infinite Sums and the Analysis of Zeroes of Analytical Functions

Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of an analytical function to obtain a few new criteria equivalent to the Riemann hypothesis. Here, the same theorem is applied to calcul ...

MDPI2023

Partial Information Sharing Over Social Learning Networks

Ali H. Sayed, Virginia Bordignon

This work addresses the problem of sharing partial information within social learning strategies. In social learning, agents solve a distributed multiple hypothesis testing problem by performing two operations at each instant: first, agents incorporate inf ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023

A NEW PROOF OF THE ERDOS-KAC CENTRAL LIMIT THEOREM

Thomas Mountford, Michael Cranston

In this paper we use the Riemann zeta distribution to give a new proof of the Erdos-Kac Central Limit Theorem. That is, if zeta(s) = Sigma(n >= 1) (1)(s)(n) , s > 1, then we consider the random variable X-s with P(X-s = n) = (1) (zeta) ( ...

Providence2023

Explainability and Graph Learning From Social Interactions

Ali H. Sayed, Stefan Vlaski, Konstantinos Ntemos, Valentina Shumovskaia

Social learning algorithms provide models for the formation of opinions over social networks resulting from local reasoning and peer-to-peer exchanges. Interactions occur over an underlying graph topology, which describes the flow of information among the ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Social Learning Under Inferential Attacks

Ali H. Sayed, Virginia Bordignon, Stefan Vlaski, Konstantinos Ntemos

A common assumption in the social learning literature is that agents exchange information in an unselfish manner. In this work, we consider the scenario where a subset of agents aims at driving the network beliefs to the wrong hypothesis. The adversaries a ...

IEEE2021

Unique decomposition of homogeneous languages and application to isothetic regions

Nicolas René Jean Ninin

A language is said to be homogeneous when all its words have the same length. Homogeneous languages thus form a monoid under concatenation. It becomes freely commutative under the simultaneous actions of every permutation group G(n) on the collection of ho ...

2019

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

Generalized Bombieri-Lagarias' Theorem And Generalized Li'S Criterion With Its Arithmetic Interpretation

We show that Li's criterion equivalent to the Riemann hypothesis, i.e., the statement that the sums k(n) = Sigma(rho)(1-(1-1/rho)(n)) over zeros of the Riemann xi-function and the derivatives lambda(n) equivalent to 1/(n-1)! d(n)/dz(n)(z(n-1) ln (xi(z)))ve ...

Springer Verlag2014

On equalities involving integrals of the logarithm of the Riemann zeta-function and equivalent to the Riemann hypothesis

By using the generalized Littlewood theorem about a contour integral involving the logarithm of an analytic function, we show how an infinite number of integral equalities involving integrals of the logarithm of the Riemann zeta-function and equivalent to ...

Springer US2012

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