Related papers: Kurepa's conjecture on the left factorial function…

We prove that any right Quillen functor between arbitrary model categories admits non trivial functorial factorizations that are similar to those of a model structure. We also prove that these factorizations can be made for lax monoidal…

We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.

In this paper we prove by induction on $n$ that any positive real number has $n$th root.

In this note we prove positivity of Maclaurin coefficients of polynomials written in terms of rising factorials and arbitrary log-concave sequences. These polynomials arise naturally when studying log-concavity of rising factorial series.…

We give a new elementary proof of the following theorem: if all critical points of a rational function g belong to the real line then there exists a fractional linear transformation L such that L(g) is a real rational function. Then we…

Building on recent work of Krueger and the second author, we prove the consistency of the Guessing Model Principle at $\omega_2$ together with the existence of an almost Kurepa Suslin tree. In particular, it is consistent that the Guessing…

We prove an analogue of the Ikehara theorem for positive non-increasing functions convergent to zero, generalising the results postulated in Diekmann, Kaper (1978, Nonlinear Anal. 2(6), 721--737) and Carr, Chmaj (2004, Proc. AMS 132(8),…

We give a reduction of the irregular case for the effective non-vanishing conjecture by virtue of the Fourier-Mukai transform. As a consequence, we reprove that the effective non-vanishing conjecture holds on algebraic surfaces.

We prove via a composition lemma, the Kotzig-Ringel-Rosa conjecture, better known as the Graceful Labeling Conjecture. We also prove via a stronger version of the composition lemma a stronger form of the Graceful Labeling Conjecture.

We show that the Fourier transform on the Jacobian of a curve interchanges "$\delta$ functions" at the curve and the theta divisor. The Torelli theorem is an immediate consequence.

We show that the naive adaptation of Malle's conjecture to fair counting functions is not true in general.

We prove Fujita's spectrum conjecture on the discreteness of pseudo-effective thresholds for polarized varieties.

We state and prove a variant of the Andr\'e-Oort conjecture for the product of 2 modular curves in positive characteristic, assuming GRH for quadratic fields.

We show that Wahl's conjecture holds in all characteristics for a minuscule G/P.

In this paper we prove the validity of Gibbons' conjecture for the quasilinear elliptic equation $ -\Delta_p u = f(u) $ on $\mathbb{R}^N.$ The result holds true for $(2N+2)/(N+2) < p < 2$ and for a very general class of nonlinearity $f$.

We prove a recent conjecture of Hadjicostas concerning a double integral formula involving the zeta and the gamma functions.

In this paper, we give an affirmative answer to a conjecture raised by Polini and Ulrich.

We prove in particular that for any sufficiently large prime $p$ there is $1\le a<p$ such that all partial quotients of $a/p$ are bounded by $O(\log p/\log \log p)$. For composite denominators a similar result is obtained. This improves the…

We show that Fueter's theorem holds for a more general class of quaternionic functions than those constructed by the Fueter's method.

Using relativized ordinal analysis, we give a proof-theoretic characterization of the provably total set-recursive-from-$\omega$ functions of KPl and related theories.