Related papers: A weighted version of Saitoh's conjecture

Using toric geometry we prove a B\'ezout type theorem for weighted projective spaces.

In this short note, we propose an unified method to derive formulas for derivations conjugated by exponential functions on an almost complex manifold. In v3, we corrected some mistakes in previous versions.

We characterize all the strongly monotypic polytopes. Hadwiger's conjecture for this class of polytopes is deduced from the characterization.

Linearized Reed-Solomon codes are defined. Higher weight distribution of those codes are determined.

In this paper, we consider sums of values of degenerate falling factorials and give a probabilistic proof of a recurrence relation for them. This may be viewed as a degenerate version of the recent probabilistic proofs on sums of powers of…

A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of extensor fields is present using algebraic and analytical tools developed in previous papers. Several important formulas are derived.

Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…

We give an a geometric interpretation of the Hasse-Arf theorem for function fields using the recently proved Oort conjecture.

In this paper we show the equivalence of the conjectures of Giuga and Agoh in a direct way which leads to a combined conjecture. This conjecture is described by a sum of fractions from which all conditions can be derived easily.

We prove the converse of Yano's extrapolation theorem for translation invariant operators.

In this paper, we prove a converse theorem for half-integral weight modular forms assuming functional equations for $L$-series with additive twists. This result is an extension of Booker, Farmer, and Lee's result in [BFL22] to the…

A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…

We present a direct proof of the second conjecture made by M. Atiyah and P. Sutcliffe for the case of convex quadrilaterals. Unlike previous work on this conjecture, our proof does not require any computer aided computations. The new proof…

This paper is devoted to a weighted version of the one-level density of the non-trivial zeros of $L$-functions, tilted by a power of the $L$-function evaluated at the central point. Assuming the Riemann Hypothesis and the ratio conjecture,…

An integral transformation relating two inequalities in Khabibullin's conjecture is found. Another proof of this conjecture for some special values of its numeric parameters is suggested.

In this paper, we prove a conjecture of Schnell in the surface case.

These brief notes record our puzzles and findings surrounding Givental's recent conjecture which expresses higher genus Gromov-Witten invariants in terms of the genus-0 data. We limit our considerations to the case of a projective line,…

In this paper, we introduce a new generalized derivative, which we term the specular derivative. We establish the Quasi-Rolles' Theorem, the Quasi-Mean Value Theorem, and the Fundamental Theorem of Calculus in light of the specular…

Recently, Gautschi introduced so-called generalized Gauss-Radau and Gauss-Lobatto formulae which are quadrature formulae of Gaussian type involving not only the values but also the derivatives of the function at the endpoints. In the…

Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.