Zobrazeno 1 - 10
of 25
pro vyhledávání: '"Kalmynin, Alexander"'
Autor:
Qiu, Yuan, Kalmynin, Alexander B.
The research in the subfield of analytic number theory around error term of summation of sigma functions possesses a history which can be dated back to the mid-19th century when Dirichlet provided an $O(\sqrt{n})$ estimation of error term of summatio
Externí odkaz:
http://arxiv.org/abs/2412.00723
Autor:
Kalmynin, Alexander
Let $h_n(v)$ be the sequence of rational functions with $$ \frac{h_n(v)}{v}-nh_n(v)+(n-1)h_{n-1}(v)-vh_{n-1}'(v)+\frac{v(v(vh_{n-1}(v))')'}{4}=0 $$ for $n>0$ and $h_0(v)=1$. We prove that $h_n(v)$ has a pole at $v=\frac{1}{n}$ if and only if $n$ is a
Externí odkaz:
http://arxiv.org/abs/2407.03002
Autor:
Kalmynin, Alexander, Konyagin, Sergei
Let $M(x)$ be the length of the largest subinterval of $[1,x]$ which does not contain any sums of two squareful numbers. We prove a lower bound \[ M(x)\gg \frac{\ln x}{(\ln\ln x)^2} \] for all $x\geq 3$. The proof relies on properties of random subse
Externí odkaz:
http://arxiv.org/abs/2303.14833
Autor:
Kalmynin, Alexander, Konyagin, Sergei
For a polynomial $f(x)\in \mathbb Z[x]$ we study an analogue of Jacobsthal function, defined by the formula \[ j_f(N)=\max_{m}\{\text{For some } x\in \mathbb N \text{ the inequality } (x+f(i),N)>1 \text{ holds for all }i\leq m\}. \] We prove a lower
Externí odkaz:
http://arxiv.org/abs/2302.00459
Autor:
Kalmynin, Alexander
Let $\mathcal L^+$ be the set of all primes $p$ for which the sums of $\left(\frac{n}{p}\right)$ over the interval $[1,N]$ are non-negative for all $N$. We prove that the estimate \[ |\mathcal L^+\cap [1,x]|\ll \frac{x}{\ln x(\ln\ln x)^{c-o(1)}} \] h
Externí odkaz:
http://arxiv.org/abs/2105.06910
Autor:
Kalmynin, Alexander
For $0\leq \alpha<1$ and prime number $p$ let $L(\alpha,p)$ be the sum of the first $[\alpha p]$ values of Legendre symbol modulo $p$. We study positivity of $L(\alpha,p)$ and prove that for $|\alpha-\frac13|<2\cdot 10^{-6}$ and for rational $\alpha\
Externí odkaz:
http://arxiv.org/abs/1911.10634
Autor:
Kalmynin, Alexander, Kosenko, Petr
We study the properties of a sequence cn defined by the recursive relation \[\frac{c_0}{n + 1}+\frac{c_1}{n + 2}+\ldots+\frac{c_n}{2n + 1}=0\] for $n>1$ and $c_0=1$. This sequence also has an alternative definition in terms of certain norm minimizati
Externí odkaz:
http://arxiv.org/abs/1901.04044
Autor:
Kalmynin, Alexander
In this paper, we prove that for any $A>0$ there exist infinitely many primes $p$ for which sums of the Legendre symbol modulo $p$ over an interval of length $(\ln p)^A$ can take large values.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/1712.08080
Autor:
Kalmynin, Alexander
We introduce a generalization of the method of S. P. Zaitsev. This generalization allows us to prove omega-theorems for the Riemann zeta function and its derivatives in some regions near the line $\mathrm{Re}\,s=1$.
Externí odkaz:
http://arxiv.org/abs/1706.07364
Autor:
Kalmynin, Alexander
We prove some new lower bounds for the counting function $\mathcal N_{\mathcal C}(x)$ of the set of Nov\'ak-Carmichael numbers. Our estimates depend on the bounds for the number of shifted primes without large prime factors. In particular, we prove t
Externí odkaz:
http://arxiv.org/abs/1706.07343