English
Related papers

Related papers: On the Balazard-Saias criterion for the Riemann Hy…

200 papers

We establish upper bounds for shifted moments of cubic and quartic Dirichlet $L$-functions under the generalized Riemann hypothesis. As an application, we prove bounds for moments of cubic and quartic Dirichlet character sums.

Number Theory · Mathematics 2025-08-21 Peng Gao , Liangyi Zhao

We address the problem of providing inference from a Bayesian perspective for parameters selected after viewing the data. We present a Bayesian framework for providing inference for selected parameters, based on the observation that…

Computation · Statistics 2015-03-13 Daniel Yekutieli

Re-randomization has gained popularity as a tool for experiment-based causal inference due to its superior covariate balance and statistical efficiency compared to classic randomized experiments. However, the basic re-randomization method,…

Methodology · Statistics 2023-09-20 Zhaoyang Liu , Tingxuan Han , Donald B. Rubin , Ke Deng

In this paper, we introduce a class of Dirichlet series defined in terms of the Riemann zeta-function, motivated by the study of their special values, and establish integral representations for these series. We also define an extension of…

Number Theory · Mathematics 2026-02-17 Takumi Noda

In this article, methods from sub-Hardy Hilbert spaces such as the de Branges-Rovnyak spaces and local Dirichlet spaces are used to investigate B\'aez-Duarte's Hilbert space reformulation of the Riemann hypothesis (RH).

Functional Analysis · Mathematics 2019-05-10 S. Waleed Noor

The proof of the conjecture of the Birch and Swinnerton - Dyer is presented in the paper. The Riemann's hypothesis on the distribution of non-trivial zeroes of the zeta-function of Riemann, previously proven, is word to prove this…

General Mathematics · Mathematics 2014-06-10 S. V. Matnyak

We prove a quantified Tauberian theorem involving Laplace-Stieltjes transform which is motivated by the work of Ingham and Karamata. For this, we consider functions which are locally of bounded variation and, therefore, get a generalisation…

Functional Analysis · Mathematics 2018-08-14 Markus Hartlapp

We substantially apply the Li criterion for the Riemann hypothesis to hold. Based upon a series representation for the sequence \{\lambda_k\}, which are certain logarithmic derivatives of the Riemann xi function evaluated at unity, we…

Mathematical Physics · Physics 2009-11-11 Mark W. Coffey

We introduce a new formulation of baryon chiral perturbation theory which improves the ultraviolet behavior of propagators and can be interpreted as a smooth cutoff regularization scheme. It is equivalent to the standard approach, preserves…

High Energy Physics - Phenomenology · Physics 2011-07-19 D. Djukanovic , M. R. Schindler , J. Gegelia , S. Scherer

We present an alternative approach to the Bayesian nonparametric analysis of conditional species richness under two-parameter Poisson Dirichlet priors. We rely on a known characterization by deletion of classes property and on results for…

Probability · Mathematics 2010-02-03 Annalisa Cerquetti

Some little considerations concerning the application of the Theory of Dirichlet Forms to stocastic variational principle on riemannian manifolds are performed

Mathematical Physics · Physics 2007-05-23 Gavriel Segre

We provide a reason for Bayesian updating, in the Bernoulli case, even when it is assumed that observations are independent and identically distributed with a fixed but unknown parameter $\theta_0$. The motivation relies on the use of loss…

Statistics Theory · Mathematics 2010-06-08 Pier Giovanni Bissiri , Stephen G. Walker

In the study of Dirichlet series with arithmetic significance there has appeared (through the study of known examples) certain expectations, namely (i) if a functional equation and Euler product exists, then it is likely that a type of…

Number Theory · Mathematics 2024-10-10 J. Brian Conrey , Amit Ghosh

Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter…

Statistics Theory · Mathematics 2018-08-28 Hedibert F. Lopes , Nicholas G. Polson

A bias-reduced estimator is proposed for the mean absolute deviation parameter of a median regression model. A workaround is devised for the lack of smoothness in the sense conventionally required in general bias-reduced estimation. A local…

Methodology · Statistics 2023-05-04 Michele Lambardi di San Miniato

We consider the Laplacian in a straight strip, subject to a combination of Dirichlet and Neumann boundary conditions. We show that a switch of the respective boundary conditions leads to a Hardy inequality for the Laplacian. As a byproduct…

Mathematical Physics · Physics 2009-03-19 Hynek Kovarik , David Krejcirik

The aim of this article is to make a contribution to the Bayesian procedure of testing precise hypotheses for parametric models. For this purpose, we define the Bayesian Discrepancy Measure that allows one to evaluate the suitability of a…

Methodology · Statistics 2022-11-21 Francesco Bertolino , Mara Manca , Monica Musio , Walter Racugno , Laura Ventura

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

Number Theory · Mathematics 2007-05-31 Yitang Zhang

The Riemann hypothesis is proved by quantum-extending the zeta Riemann function to a quantum mapping between quantum $1$-spheres with quantum algebra $A=\mathbb{C}$, in the sense of A. Pr\'astaro \cite{PRAS01, PRAS02}. Algebraic topologic…

General Mathematics · Mathematics 2015-10-28 Agostino Prástaro

In this note, we give a simple proof that the Riemann Hypothesis is unprovable in any reasonable axiom system.

General Mathematics · Mathematics 2011-11-24 Craig Alan Feinstein