A. Kalmynin

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20172021

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math.NT2021

Quadratic characters with positive partial sums

Alexander Kalmynin

Let $L^{+}$ be the set of all primes $p$ for which the sums of $(\frac{n}{p})$ over the interval $[1, N]$ are non-negative for all $N$ . We prove that the estimate…

math.NT2019

Orthorecursive expansion of unity

Alexander Kalmynin, Petr Kosenko

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…

math.NT2017

Large values of short character sums

Alexander Kalmynin

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 l…

math.NT2017

Omega-theorems for the Riemann zeta function and its derivatives near the line $Re s = 1$

Alexander Kalmynin

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 region…

math.NT2017

Novák-Carmichael numbers and shifted primes without large prime factors

Alexander Kalmynin

We prove some new lower bounds for the counting function $N_{C} (x)$ of the set of Novák-Carmichael numbers. Our estimates depend on the bounds for the number of s…

Quadratic characters with positive partial sums

Orthorecursive expansion of unity

Large values of short character sums

Omega-theorems for the Riemann zeta function and its derivatives near the line Res=1

Novák-Carmichael numbers and shifted primes without large prime factors

Omega-theorems for the Riemann zeta function and its derivatives near the line $Re s = 1$