相关论文: A special case of a conjecture of Hellerstein, She…

Shanks conjectured that $\zeta ' (\rho)$, where $\rho$ ranges over non-trivial zeros of the Riemann zeta function, is real and positive in the mean. We present a history of this problem, including a generalisation to all higher-order…

We give a derivative version of the relative trace formula on PGL(2) studied in our previous work, and obtain a formula of an average of central values (derivatives) of automorphic $L$-functions for Hilbert cusp forms. As an application, we…

We show that complex geometric features of Teichmuller spaces create explicitly the extremals of generic homogeneous holomorphic functionals on univalent functions. In particular this gives proofs of the well-known Zalcman and Bieberbach…

Let $K$ be an algebraically closed field of characteristic zero, $\delta$ a nonzero $\mathcal{E}$-derivation of $K[x]$. We first prove that $\operatorname{Im}\delta$ is a Mathieu-Zhao space of $K[x]$ in some cases. Then we prove that LFED…

The Weitzenboeck theorem states that the algebra of constants of a linear locally nilpotent derivation of the polynomial algebra K[Z]=K[z_1,...,z_m] in m variables over a field K of characteristic 0 is finitely generated. If m=2n and the…

It is be shown that the sequence of Bernstein polynomials for a function of several variables converges to this function uniformly along with every partial derivative of any order, provided that the latter derivative is well defined and…

The monodromy conjecture is an umbrella term for several conjectured relationships between poles of zeta functions, monodromy eigenvalues and roots of Bernstein-Sato polynomials in arithmetic geometry and singularity theory. Even the…

We prove the Weinstein conjecture for non-trivial contact connected sums under either of two topological conditions: non-trivial fundamental group or torsion-free homology.

In this paper, we investigate meromorphic solutions of certain nonlinear partial differential equations in several complex variables involving differential and functional operators. Let $f$ be a non-constant meromorphic function in…

Let p be a prime and F a totally real field in which p is unramified. We consider mod p Hilbert modular forms for F, defined as sections of automorphic line bundles on Hilbert modular varieties of level prime to p in characteristic p. For a…

We generalize Witten's conjectured formula relating Donaldson and Seiberg-Witten invariants to manifolds of non-simple type, via equivariant localization techniques. This approach does not use the theory of non-abelian monopoles, but works…

Assuming the Riemann hypothesis, we obtain a formula for the mean value of the $k$-derivative of $\zeta'/\zeta$, depending on the pair correlation of zeros of the Riemann zeta-function. This formula allows us to obtain new equivalences to…

In this note, we show that any epimorphism originating at a von Neumann regular ring (not necessary commutative) is a universal localization. As an application, we prove that the Telescope Conjecture holds for the unbounded derived…

In a paper of Bosio and Meersseman (Real quadrics in Cn, complex manifolds and convex polytopes) the following is conjectured: If P is dual neighborly, then Zp is diffeomorphic to the connected sum of products of spheres. In this paper a…

In this article, following an insight of Kontsevich, we extend the famous Weil conjecture (as well as the strong form of the Tate conjecture) from the realm of algebraic geometry to the broad noncommutative setting of dg categories. As a…

In [1] M. Baker and S. Norine developed a theory of divisors and linear systems on graphs, and proved a Riemann-Roch Theorem for these objects (conceived as integer-valued functions on the vertices). In [2] and [3] the authors generalized…

In this short manuscript, we will put some light on the different outcomes when two non-constant meromorphic functions share a value with prescribed weight two.

We present a study of real Hurwitz numbers enumerating a special kind of real meromorphic functions, which we call simple framed purely real functions. We deduce partial differential equations of cut-and-join type for generating functions…

We prove a conjecture by A. Kuznetsov and A. Polishchuk on the existence of some particular full exceptional collections in bounded derived categories of coherent sheaves on Grassmannian varieties.

We answer a question of Slaman and Steel by showing that a version of Martin's conjecture holds for all regressive functions on the hyperarithmetic degrees. A key step in our proof, which may have applications to other cases of Martin's…