Related papers: A Better Lower Bound Estimation of Brennan's Conje…
In this paper, we prove a conjecture of Schnell in the surface case.
We derive a lower bound for a second moment of the reciprocal of the derivative of the Riemann zeta-function averaged over the zeros of the zeta-function that is half the size of the conjectured value. Our result is conditional upon the…
We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].
We present a formulation of the Collatz conjecture that is potentially more amenable to modeling and analysis by automated termination checking tools.
We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
We survey recent developments on the Restriction conjecture.
A descent conjecture of Wittenberg [Wit24, Conjecture 3.7.4] predicts that if all the twists of a rationally connected torsor over a smooth base satisfy weak approximation with Brauer-Manin obstruction, then so does the base. We give an…
We give a short probabilistic (a Brownian motion) proof of the Riemann hypothesis based on some surprising, unexpected and deep algebraic conjecture (MAC in short) concerning the relation between the Riemann zeta $\xi$ and a trivial zeta…
This paper takes a new step in the direction of proving the Duffin-Schaeffer Conjecture for measures arbitrarily close to Lebesgue. The main result is that under a mild `extra divergence' hypothesis, the conjecture is true.
In this short note we improve the best to date bound in Godbersen's conjecture, and show some implications for unbalanced difference bodies.
In this short survey article, we aim to provide an up to date information on the progress made towards Schurs exponent conjecture and related conjectures. We also mention the connection between Schurs exponent conjecture and Noether's…
In this paper, we derive a more precise version of the Strong Pair Correlation Conjecture on the zeros of the Riemann zeta function under Riemann Hypothesis and Twin Prime Conjecture.
We make the final step to give a proof for the Brannan's conjecture. The basic tool of the study is a Mac-Laurin development and an adequately estimation of an integral.
An approximate formula for the partitions of Goldbach's Conjecture is derived using Prime Number Theorem and a heuristic probabilistic approach. A strong form of Goldbach's conjecture follows in the form of a lower bounding function for the…
We give a counterexample to a recently conjectured variant of the Penrose inequality.
In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.
We prove a new lower bound for the Frobenius norm of the inverse of an non-negative matrix. This bound is only a modest improvement over previous results, but is sufficient for fully resolving a conjecture of Harwitz and Sloane, commonly…
In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.
In the present note, we give a short proof of Brennan's conjecture in the special case of continuous semigroups of holomorphic functions. We apply classical techniques of complex analysis in conjunction with recent results on…