Related papers: A theorem on shifted Hankel determinants

The purpose of this paper is to compute asymptotically Hankel determinants for weights that are supported in a semi-infinite interval.The main idea is to reduce the problem to determinants of other operators whose determinant asymptotics…

We evaluate the Hankel determinants of the convolution powers of Motzkin numbers for $r\leq 27$ by finding shifted periodic continued fractions, which arose in application of Sulanke and Xin's continued fraction method. We also conjecture…

We present a probabilistic proof of Euler's pentagonal number theorem based on a shuffling model.

We prove a compatibility theorem between the Stark conjecture and the Harris-Venkatesh conjecture for imaginary dihedral modular forms of weight $1$. The key technical input is a general two-variable $\mathrm{PGL}_2$ Siegel-Weil formula…

We develop the $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic twist of modular $L$-functions using multiple Dirichlet series under the generalized Riemann…

After a short survey about Schroeder numbers and some generalizations which I call Schroeder-like numbers I study some q-analogues which have simple Hankel determinants.

We prove a conjecture due to Y. Last on Jacobi matrices.

We prove in this paper the Ax-Schanuel conjecture for all admissible variations of mixed Hodge structures.

We aim to prove a twisted version of the Osborne conjecture obtained by Hecht and Schmid in their 1983 Acta Mathematica paper. Bergeron and Clozel (2013) have considered a special case, and we generalize their method to our setting.

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

We prove Weibel's conjecture for twisted $K$-theory when twisting by a smooth proper connective dg-algebra. Our main contribution is showing we can kill a negative twisted $K$-theory class using a projective birational morphism (in the same…

We present some new results on the cohomology of a large scope of SL\_2-groups in degrees above the virtual cohomological dimension; yielding some partial positive results for the Quillen conjecture in rank one. We combine these results…

It is a longstanding conjecture that for a finite group $G$, the exponent of the second homology group $H_2(G, \mathbb{Z})$ divides the exponent of $G$. In this paper, we prove this conjecture for $p$-groups of class at most $p$, finite…

This paper sets out to introduce the generalized derangement polynomials of order $r $. It then proceeds to establish various identities associated with these polynomials, along with providing recurrence relations for derangement…

A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.

We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.

We reformulate a conjecture of Deligne on 1-motives by using the integral weight filtration of Gillet and Soul\'e on cohomology, and prove it. This implies the original conjecture up to isogeny. If the degree of cohomology is at most two,…