Related papers: Some corrections to an old paper

We correct the proofs of the main theorems in our paper "Limit theorems for Betti numbers of random simplicial complexes".

A gap in the proof of Theorem 3.5 in the paper ``A new iteration process for approximation of common fixed points for finite families of total asymtotically nonexpansive mappings". Int. J. Math. Math. Sci. vol. 2009,…

We continue the work of [4, 2, 3], in which we discuss published assertions that are incorrect or incorrectly proven; that are severely limited or reduce to triviality; or that we improve upon.

We study inequalities between general integral moduli of continuity of a function and the tail integral of its Fourier transform. We obtain, in particular, a refinement of a result due to D. B. H. Cline [2] (Theorem 1.1 below). We note that…

We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ingredients. The first is Szemeredi's theorem, which asserts that any subset of the integers of positive density contains progressions of…

We generalize our theorems in "Mirror Principle I" to a class of balloon manifolds. Many of the results are proved for convex projective manifolds. In a subsequent paper, Mirror Principle III, we will extend the results to projective…

We correct here two errors in our earlier paper "An algebraic model for finite loop spaces" [arXiv:1212.2033]

We continue our investigations of bilinear sums with modular square roots and the large sieve for square moduli in our recent article "On bilinear sums with modular square roots and applications II", arXiv:2603.00768. In the present…

We explain and correct a mistake in Section 2.6 and Appendix C of the first and second author's paper "Representation Growth and Rational Singularities of the Moduli Space of Local Systems" arXiv:1307.0371.

We verify the Hardy-Littlewood conjecture on primes in quadratic progressions on average. The results in the present paper significantly improve those of a previous paper of the authors(arXiv:math.NT/0605563).

Some mistaken reasonings at the end of the paper omitted.

Green and Tao proved that the primes contains arbitrarily long arithmetic progressions. We show that, essentially the same proof leads to the following result: The primes in an short interval contains many arithmetic progressions of any…

We address the prime geodesic theorem in arithmetic progressions, and resolve conjectures of Golovchanski\u{\i}-Smotrov (1999). In particular, we prove that the traces of closed geodesics on the modular surface do not equidistribute in the…

The (extended) AGM postulates for belief revision seem to deal with the revision of a given theory K by an arbitrary formula, but not to constrain the revisions of two different theories by the same formula. A new postulate is proposed and…

In their comment, Murphy et al. (arxiv:0708.3677) criticize the fitting procedure we used in two previous papers [Srianand et al. 2004(Paper I) and Chand et al. 2004 (Paper II)] and conclude that the above papers offers no stringent test to…

We correct an error in Lemma 4.4 and its application in Theorem 4.5 in our paper ``Kudla's Modularity Conjecture and Formal Fourier-Jacobi Series''.

We correct the second main theorem of the previous paper "A perturbation of the Dunkl harmonic oscillator on the line", by the first two authors. The corrections concern mainly certain estimates, which were also improved by adding more…

The property 4 in Proposition 2.3 from the paper "Some remarks on Davie's uniqueness theorem" is replaced with a weaker assertion which is sufficient for the proof of the main results. Technical details and improvements are given.

In this paper, the second of two companion pieces, we explore novel philosophical questions raised by recent progress in large language models (LLMs) that go beyond the classical debates covered in the first part. We focus particularly on…

We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.