Related papers: Change of variable in Riemann integration revisite…
We derive a general change of variables formula for score functions, showing that for a smooth, invertible transformation $\mathbf{y} = \phi(\mathbf{x})$, the transformed score function $\nabla_{\mathbf{y}} \log q(\mathbf{y})$ can be…
A recognized trend of research investigates generalizations of the Hadamard's inversion theorem to functions that may fail to be differentiable. In this vein, the present paper explores some consequences of a recent result about the…
We show that the Generalized Riemann Hypothesis for all Dirichlet L-functions is a consequence of certain conjectural properties of the zeros of the Riemann zeta function. Conversely, we prove that the zeros of $\zeta(s)$ satisfy those…
Baez-Duarte reformulated the Riemann hypothesis as a statement about a Hilbert space distance, involving the integer dilations of the "fractional part" function. Under the assumption of the Riemann hypothesis, we improve on the currently…
We give a revised version of Schmidt's treatment of forms in many variables, which allows us to prove a Hasse principle under more lenient conditions on the number of variables than what had previously been thought possible with these…
A simple heuristic proof of an integral identity recently derived (Glasser ML 2011 J. Phys. A: Math. Theor. 44 225202) is presented.
By using the generalized Bernoulli numbers, we deduce new integral representations for the Riemann zeta function at positive odd-integer arguments. The explicit expressions enable us to obtain criteria for the dimension of the vector space…
Inspired by the recent work by R.Pal et al., we give further refined inequalities for a convex Riemann integrable function, applying the standard Hermite-Hadamard inequality. Our approach is different from their one in \cite{PSMA2016}. As…
We introduce a new, elementary method for studying random differences in arithmetic progressions and convergence phenomena along random sequences of integers. We apply our method to obtain significant improvements on previously known…
In this short note I present a tauberian conjecture that I consider to be the simplest and the best tauberian reformulation of RH using good variation theory. The method applies also to the Grand Riemann Hypothesis.
A proposed solution to the Riemann Hypothesis
Regression adjustments are often made to experimental data. Since randomization does not justify the models, bias is likely; nor are the usual variance calculations to be trusted. Here, we evaluate regression adjustments using Neyman's…
We obtain another proof of Hermite's integral for the Hurwitz zeta function.
In this note, we give an exposition of the construction of Seiberg-Witten invariants.
In this review paper, we describe the use of couplings in several different mathematical problems. We consider the total variation norm, maximal coupling, and the $\bar{d}$-distance. We present a detailed proof of a result recently proved:…
We present an elementary proof of a general version of Montel's theorem in several variables which is based on the use of tensor product polynomial interpolation. We also prove a Montel-Popoviciu's type theorem for functions…
We obtain the rigorous uniform asymptotics of a particular integral where a stationary point is close to an endpoint. There exists a general method introduced by Bleistein for obtaining uniform asymptotics in this situation. However, this…
We prove a sharp integral inequality for the dyadic maximal operator and give as an application another proof for the computation of its Bellman function of three variables.
We propose an estimator of the Hilbert-Schmidt Independence Criterion obtained from an appropriate modification of the usual estimator. We then get asymptotic normality of this estimator both under independence hypothesis and under the…
Using the notion of the truncated variation we obtain a new theorem on the existence and estimation of the Riemann-Stieltjes integral. As a special case of this theorem we obtain an improved version of the Lo\'{e}ve-Young inequality for the…