Related papers: Generalized Sato-Tate and quadratic residues

In 1995, Ehud de Shalit proved an analogue of a conjecture of Mazur--Tate for the modular Jacobian $J_0(p)$. His main result was valid away from the Eisenstein primes. We complete the work of de Shalit by including the Eisenstein primes,…

Let p > 2 be prime. We use purely local methods to determine the possible reductions of certain two-dimensional crystalline representations, which we call "pseudo-Barsotti-Tate representations", over arbitrary finite extensions of the…

We obtain new results about the representation of almost all residues modulo a prime $p$ by a product of a small integer and also an element of small multiplicative subgroup of $({\mathbb Z}/p{\mathbb Z})^*$. These results are based on some…

In this talk an introduction to generalized parton distributions is given. Recent developments are shortly reviewed, including non-perturbative calculations, phenomenological aspects and evaluation of higher order perturbative and power…

In this paper, we will first summarize known results concerning continued fractions. Then we will limit our consideration to continued fractions of quadratic numbers. The second author described periods and sometimes precise form of…

We find arbitrarily large configurations of irreducible polynomials over finite fields that are separated by low degree polynomials. Our proof adapts an argument of Pintz from the integers, in which he combines the methods of…

We prove that the Tate conjecture for divisors is ''generically true'' for mod p reductions of complex projective varieties with $h^{2, 0} = 1$, under a mild assumption on moduli. By refining this general result, we establish a new case of…

It is known that every relatively pseudocomplemented lattice is residuated and, moreover, it is distributive. Unfortunately, non-distributive lattices with a unary operation satisfying properties similar to relative pseudocomplementation…

Combinatorial $t$-designs have been an interesting topic in combinatorics for decades. It was recently reported that the image sets of a fixed size of certain special polynomials may constitute a $t$-design. Till now only a small amount of…

Two $q$-supercongruences of truncated basic hypergeometric series containing two free parameters are established by employing specific identities for basic hypergeometric series. The results partly extend two $q$-supercongruences that were…

Let p be a prime = 3 (mod 4). A number of elegant number-theoretical properties of the sums T(p) = \sqrt{p}sum_{n=1}^{(p-1)/2} tan(n^2\pi/p) and C(p) = \sqrt{p}sum_{n=1}^{(p-1)/2} cot(n^2\pi/p) are proved. For example, T(p) equals p times…

We derive a combinatorial identity which is useful in studying the distribution of Fourier coefficients of L-functions by allowing us to pass from knowledge of moments of the coefficients to the distribution of the coefficients.

We present a conjecture on the irreducibility of the tensor products of fundamental representations of quantized affine algebras. This conjecture implies in particular that the irreducibility of the tensor products of fundamental…

Using a quadratic version of the Bott residue theorem, we give a quadratic refinement of the count of twisted cubic curves on hypersurfaces and complete intersections in a projective space.

The goal of this note is to give a characterization of generalized quaternion $2$-groups by using their posets of cyclic subgroups.

In this paper, we extend the result of Fujii on the second moment of $S(t+h) - S(t)$ to longer range of $h$ under the Riemann Hypothesis and an quantitative form of the Twin Prime Conjecture.

We show a residues formula for maps generically transversal to regular holomorphic distributions.

We prove that there are at most 13 real quadratic fields that admit a ternary universal quadratic lattice, thus establishing a strong version of Kitaoka's Conjecture for quadratic fields. More generally, we obtain explicit upper bounds on…

I review progress on selected issues connected with generalized parton distributions. Topics range from the description of hard exclusive reactions to the spatial distribution of quarks in the nucleon and the contribution of their orbital…

We give a parameterized generalization of the sum formula for quadruple zeta values. The generalization has four parameters, and is invariant under a cyclic group of order four. By substituting special values for the parameters, we also…