Publications associées à On equalities involving integrals of the logarithm of the Riemann zeta-function and equivalent to the 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

BPS invariants from p-adic integrals

Dimitri Stelio Wyss, Francesca Carocci, Giulio Orecchia

We define p-adic BPS or pBPS invariants for moduli spaces M-beta,M-chi of one-dimensional sheaves on del Pezzo and K3 surfaces by means of integration over a non-archimedean local field F. Our definition relies on a canonical measure mu can on the F-analyt ...

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

Serguei Sekatski

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

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) ( ...

Amer Mathematical Soc2023

ALMOST EVERYWHERE NONUNIQUENESS OF INTEGRAL CURVES FOR DIVERGENCE-FREE SOBOLEV VECTOR FIELDS

Massimo Sorella

We construct divergence-free Sobolev vector fields in C([0,1];W-1,W-r(T-d;Rd)) with r < d and d\geq 2 which simultaneously admit any finite number of distinct positive solutions to the continuity equation. These vector fields are then shown to have at leas ...

Siam Publications2023

Quadrature-free immersed isogeometric analysis

Pablo Antolin Sanchez, Thibaut Hirschler

This paper presents a novel method for solving partial differential equations on three-dimensional CAD geometries by means of immersed isogeometric discretizations that do not require quadrature schemes. It relies on a newly developed technique for the eva ...

SPRINGER2022

On the Mordell-Weil lattice of y(2) = x(3) + bx plus t(3n+1) in characteristic 3

Gauthier Leterrier

We study the elliptic curves given by y(2) = x(3) + bx + t(3n+1) over global function fields of characteristic 3 ; in particular we perform an explicit computation of the L-function by relating it to the zeta function of a certain superelliptic curve u(3) ...

SPRINGER INT PUBL AG2022

A Functional Perspective on Information Measures

Amedeo Roberto Esposito

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

EPFL2022

Fluctuation estimates for the multi-cell formula in stochastic homogenization of partitions

Matthias Ruf

In this paper we derive quantitative estimates in the context of stochastic homogenization for integral functionals defined on finite partitions, where the random surface integrand is assumed to be stationary. Requiring the integrand to satisfy in addition ...

2022

Nothing New Under the Sun: Novelty Constructs and Measures in Social Studies

Davide Bavato

The concept of novelty is central to questions of creativity, innovation, and discovery. Despite the prominence in scientific inquiry and everyday discourse, there is a chronic ambiguity over its meaning and a surprising variety of empirical measures, whic ...

Emerald Publishing Limited2022

On the stress tensor light-ray operator algebra

Grégoire Olivier Mathys, Matthew Thomas Walters, Alexandre Mathieu Frédéric Belin

We study correlation functions involving generalized ANEC operators of the form integral dx-x-n+2T--x -> in four dimensions. We compute two, three, and ...

Springer Nature2021

The fourth moment of individual Dirichlet L-functions on the critical line

Berke Topacogullari

We prove an asymptotic formula for the second moment of a product of two Dirichlet L-functions on the critical line, which has a power saving in the error term and which is uniform with respect to the involved Dirichlet characters. As special cases we give ...

2021

Integral Convexity And Parabolic Systems

Bernard Dacorogna

In this work we give optimal, i.e., necessary and sufficient, conditions for integrals of the calculus of variations to guarantee the existence of solutions-both weak and variational solutions-to the associated L-2-gradient flow. The initial values are mer ...

SIAM PUBLICATIONS2020

Constraint-aware neural networks for Riemann problems

Jan Sickmann Hesthaven, Deep Ray

Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satisfied to obtai ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

Fast assembly of Galerkin matrices for 3D solid laminated composites using finite element and isogeometric discretizations

Pablo Antolin Sanchez

This work presents a novel methodology for speeding up the assembly of stiffness matrices for laminate composite 3D structures in the context of isogeometric and finite element discretizations. By splitting the involved terms into their in-plane and out-of ...

2020

Loops in AdS: from the spectral representation to position space

Din Carmi

We compute a family of scalar loop diagrams in AdS. We use the spectral representation to derive various bulk vertex/propagator identities, and these identities enable to reduce certain loop bubble diagrams to lower loop diagrams, and often to tree- level ...

Springer Nature2020

Slope-Space Integrals for Specular Next Event Estimation

Wenzel Alban Jakob, Tizian Lucien Zeltner, Guillaume Rémi Bruno Loubet

Monte Carlo light transport simulations often lack robustness in scenes containing specular or near-specular materials. Widely used uni- and bidirectional sampling strategies tend to find light paths involving such materials with insufficient probability, ...

ASSOC COMPUTING MACHINERY2020

The index of singular zeros of harmonic mappings of anti-analytic degree one

Robert Gerhard Jérôme Luce

We study harmonic mappings of the form , where h is an analytic function. In particular, we are interested in the index (a generalized multiplicity) of the zeros of such functions. Outside the critical set of f, where the Jacobian of f is non-vanishing, it ...

TAYLOR & FRANCIS LTD2021

Giant non-linear susceptibility of hydrogenic donors in silicon and germanium

Gabriel Aeppli

Implicit summation is a technique for the conversion of sums over intermediate states in multiphoton absorption and the high-order susceptibility in hydrogen into simple integrals. Here, we derive the equivalent technique for hydrogenic impurities in multi ...

Springer2019