Zobrazeno 1 - 10
of 636
pro vyhledávání: '"Zaharescu, Alexandru"'
We introduce and study arithmetic polygons. We show that these arithmetic polygons are connected to triples of square pyramidal numbers. For every odd $N\geq3$, we prove that there is at least one arithmetic polygon with $N$ sides. We also show that
Externí odkaz:
http://arxiv.org/abs/2411.08398
Let $p$ be an odd prime, and let $\omega$ be a primitive $p$th root of unity. In this paper, we introduce a metric on the cyclotomic field $K=\mathbb{Q}(\omega)$. We prove that this metric has several remarkable properties, such as invariance under t
Externí odkaz:
http://arxiv.org/abs/2410.22687
Autor:
Cobeli, Cristian, Zaharescu, Alexandru
For any odd prime $p$ and any integer $N\ge 0$, let $\mathcal{V}(p,N)$ be the set of vertices of the cyclotomic box $\mathscr{B} = \mathscr{B}(p,N)$ of edge size $2N$ and centered at the origin $O$ of the ring of integers $\mathbb{Z}[\omega]$ of the
Externí odkaz:
http://arxiv.org/abs/2410.14473
Autor:
Basak, Debmalya, Zaharescu, Alexandru
Assuming the Generalized Riemann Hypothesis, it is known that at least half of the central values $L(\frac{1}{2},\chi)$ are non-vanishing as $\chi$ ranges over primitive characters modulo $q$. Unconditionally, this is known on average over both $\chi
Externí odkaz:
http://arxiv.org/abs/2409.12474
The ternary Goldbach conjecture states that every odd number $m \geqslant 7$ can be written as the sum of three primes. We construct a set of primes $\mathbb{P}$ defined by an expanding system of admissible congruences such that almost all primes are
Externí odkaz:
http://arxiv.org/abs/2409.08968
The iterated composition of two operators, both of which are involutions and translation invariant, partitions the set of lattice points in the plane into an infinite sequence of discrete parabolas. Each such parabola contains an associated stairway-
Externí odkaz:
http://arxiv.org/abs/2408.01864
We study the pair correlation between zeros of a shifted auxiliary $ L $-function attached to a non-CM newform, the scale of which is a fixed constant. We prove an unconditional asymptotic result for the pair correlation and introduce a simplicity hy
Externí odkaz:
http://arxiv.org/abs/2407.14656
We study a class of approximations to the Riemann zeta function introduced earlier by the second author on the basis of Euler product. This allows us to justify Euler Product Sieve for generation of prime numbers. Also we show that Bounded Riemann Hy
Externí odkaz:
http://arxiv.org/abs/2406.00786
For certain families of $L$-functions, we prove that if each $L$-function in the family has only real zeros in a fixed yet arbitrarily small neighborhood of $s=1$, then one may considerably improve upon the known results on Landau-Siegel zeros. Sarna
Externí odkaz:
http://arxiv.org/abs/2404.16003
Autor:
Cobeli, Cristian, Zaharescu, Alexandru
We introduce a double-folded operator that, upon iterative application, generates a dynamical system with two types of trajectories: a cyclic one and, another that grows endlessly on parabolas. These trajectories produce two distinct partitions of th
Externí odkaz:
http://arxiv.org/abs/2403.14894