Publications related to Riemann zeta function

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

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

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

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

Neural Energy Casimir Control for Port-Hamiltonian Systems

Giancarlo Ferrari Trecate, Muhammad Zakwan, Liang Xu

The energy Casimir method is an effective controller design approach to stabilize port-Hamiltonian systems at a desired equilibrium. However, its application relies on the availability of suitable Casimir and Lyapunov functions, whose computation are gener ...

2022

Nonperturbative Mellin Amplitudes

João Pedro Alves Da Silva

Conformal field theory lies at the heart of two central topics in theoretical high energy physics: the study of quantum gravity and the mapping of quantum field theories through the renormalization group. In this thesis we explore a technique to study conf ...

EPFL2021

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

Nonperturbative Mellin amplitudes: existence, properties, applications

João Miguel Augusto Penedones Fernandes, Alexander Zhiboedov, João Pedro Alves Da Silva

We argue that nonperturbative CFT correlation functions admit a Mellin amplitude representation. Perturbative Mellin representation readily follows. We discuss the main properties of nonperturbative CFT Mellin amplitudes: subtractions, analyticity, unitari ...

Springer Nature2020

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

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

Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations

Elisabetta Chiodaroli

We study the Riemann problem for multidimensional compressible isentropic Euler equations. Using the framework developed in Chiodaroli et al (2015 Commun. Pure Appl. Math. 68 1157-90), and based on the techniques of De Lellis and Szekelyhidi (2010 Arch. Ra ...

IOP PUBLISHING LTD2018

Primary invariants of Hurwitz Frobenius manifolds

Nicolas Gerson Orantin

Hurwitz spaces parameterizing covers of the Riemann sphere can be equipped with a Frobenius structure. In this review, we recall the construction of such Hurwitz Frobenius manifolds as well as the correspondence between semisimple Frobenius manifolds and t ...

AMER MATHEMATICAL SOC2018

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

On Short Sums Of Trace Functions

Philippe Michel, Chandra Sekhar Raju

We consider sums of oscillating functions on intervals in cyclic groups of size close to the square root of the size of the group. We first prove non-trivial estimates for intervals of length slightly larger than this square root (bridging the "Polya-Vinog ...

Annales Inst Fourier2017

Conformal Mapping of Impedance Stability Models for System-Level Dynamics Assessments

Drazen Dujic, Francisco Daniel Freijedo Fernández, Uzair Javaid

Impedance stability methods are suitable for assessing the dynamics of power converters controllers, but also for ac/dc microgrids system level studies. This work proposes the combination of impedance modeling and conformal mapping for the identification o ...

2017

Non-convex, non-local functionals converging to the total variation

Hoài-Minh Nguyên

We present new results concerning the approximation of the total variation, integral(Omega)vertical bar del u vertical bar, of a function u by non-local, non-convex functionals of the form Lambda delta(u) = integral(Omega)integral(Omega)delta phi(vertical ...

Elsevier2017

Partition function on spheres: How to use zeta function regularization

Alexander Monin

It is known that not all summation methods are linear and stable. Zeta function regularization is in general nonlinear. However, in some cases formal manipulations with zeta function regularization (assuming linearity of sums) lead to correct results. We c ...

American Physical Society2016

An Offline-Online Riemann Solver for One-Dimensional Systems of Conservation Laws

Alfio Quarteroni

In this paper, we present an exact Riemann solver for one-dimensional systems of conservation laws. The method is based on an offline-online computational decomposition. During the offline stage, we generate an accurate surrogate model for the solution to ...

Springer Singapore Pte Ltd2016