Publications related to Riemann hypothesis

On the Sums over Inverse Powers of Zeros of the Hurwitz Zeta Function and Some Related Properties of These Zeros

Recently, we have applied the generalized Littlewood theorem concerning contour integrals of the logarithm of the analytical function to find the sums over inverse powers of zeros for the incomplete gamma and Riemann zeta functions, polygamma functions, an ...

MDPI2024

Some Mordell-Weil lattices and applications to sphere packings

Gauthier Leterrier

We provide new explicit examples of lattice sphere packings in dimensions 54, 55, 162, 163, 486 and 487 that are the densest known so far, using Kummer families of elliptic curves over global function fields.In some cases, these families of elliptic curves ...

EPFL2024

Social Opinion Formation and Decision Making Under Communication Trends

Ali H. Sayed, Mert Kayaalp, Virginia Bordignon

This work studies the learning process over social networks under partial and random information sharing. In traditional social learning models, agents exchange full belief information with each other while trying to infer the true state of nature. We stud ...

Piscataway2024

An extension of the stochastic sewing lemma and applications to fractional stochastic calculus

Toyomu Matsuda

We give an extension of Le's stochastic sewing lemma. The stochastic sewing lemma proves convergence in

L_m

of Riemann type sums

\sum _{[s,t] \in \pi } A_{s,t}

for an adapted two-parameter stochastic process A, under certain conditions on the moments o ...

Cambridge Univ Press2024

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

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

Volkan Cevher

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

Power variations in fractional Sobolev spaces for a class of parabolic stochastic PDEs

Robert Dalang, Carsten Hao Ye Chong

We consider a class of parabolic stochastic PDEs on bounded domains D c Rd that includes the stochastic heat equation but with a fractional power gamma of the Laplacian. Viewing the solution as a process with values in a scale of fractional Sobolev spaces ...

INT STATISTICAL INST2023

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, Valentina Shumovskaia, Stefan Vlaski, Konstantinos Ntemos

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

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On the Sums over Inverse Powers of Zeros of the Hurwitz Zeta Function and Some Related Properties of These Zeros

Some Mordell-Weil lattices and applications to sphere packings

Social Opinion Formation and Decision Making Under Communication Trends

An extension of the stochastic sewing lemma and applications to fractional stochastic calculus

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

Partial Information Sharing Over Social Learning Networks

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

Power variations in fractional Sobolev spaces for a class of parabolic stochastic PDEs

A NEW PROOF OF THE ERDOS-KAC CENTRAL LIMIT THEOREM

Explainability and Graph Learning From Social Interactions

Social Opinion Formation and Decision Making Under Communication Trends

On the Sums over Inverse Powers of Zeros of the Hurwitz Zeta Function and Some Related Properties of These Zeros

Partial Information Sharing Over Social Learning Networks

A NEW PROOF OF THE ERDOS-KAC CENTRAL LIMIT THEOREM

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

Some Mordell-Weil lattices and applications to sphere packings

Power variations in fractional Sobolev spaces for a class of parabolic stochastic PDEs

An extension of the stochastic sewing lemma and applications to fractional stochastic calculus

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

Explainability and Graph Learning From Social Interactions