Zobrazeno 1 - 10
of 1 595
pro vyhledávání: '"11N37"'
Publikováno v:
Acta Arithmetica, 216.4(2024), 291-327
Let $\Delta_{k}(x)$ be the error term in the classical asymptotic formula for the sum $\sum_{n\leq x}d_{k}(n)$, where $d_{k}(n)$ is the number of ways $n$ can be written as a product of $k$ factors. We study the analytic properties of the Dirichlet s
Externí odkaz:
http://arxiv.org/abs/2412.11069
Autor:
Da Conceição, Joaquim Cera
We consider the set of monic irreducible polynomials $P$ over a finite field $\mathbb{F}_q$ such that the multiplicative order modulo $P$ of some a in $\mathbb{F}_q(T)$ is divisible by a fixed positive integer $d$. Call $R_q(a,d)$ this set. We show t
Externí odkaz:
http://arxiv.org/abs/2412.09107
In a recent article, Donoso, Le, Moreira and Sun studied sets of recurrence for actions of the multiplicative semigroup $(\mathbb{N}, \times)$ and provided some sufficient conditions for sets of the form $S=\{(an+b)/(cn+d) \colon n \in \mathbb{N} \}$
Externí odkaz:
http://arxiv.org/abs/2412.03504
Parity results concerning the generalized divisor function involving small prime factors of integers
Autor:
Alladi, Krishnaswami, Goswami, Ankush
Let $\nu_y(n)$ denote the number of distinct prime factors of $n$ that are $
Externí odkaz:
http://arxiv.org/abs/2412.03088
Autor:
Chourasiya, Shashi
Let $N(\sigma,T)$ denote the number of nontrivial zeros of the Riemann zeta function with real part greater than $\sigma$ and imaginary part lying between $0$ and $T$. In this article, we provide an explicit version of Carlson's zero density estimate
Externí odkaz:
http://arxiv.org/abs/2412.02068
For a given integer $m$ and any residue $a \pmod{m}$ that can be written as a sum of 3 squares modulo $m$, we show the existence of infinitely many integers $n \equiv a \pmod{m}$ such that the number of representations of $n$ as a sum of three square
Externí odkaz:
http://arxiv.org/abs/2412.01988
Autor:
Lau, Yuk-Kam, Lee, Wonwoong
Let $d(n)$ be the number of divisors of $n$. We investigate the average value of $d(a_f(p))^r$ for $r$ a positive integer and $a_f(p)$ the $p$-th Fourier coefficient of a cuspidal eigenform $f$ having integral Fourier coefficients, where $p$ is a pri
Externí odkaz:
http://arxiv.org/abs/2411.17210
Autor:
Zudilin, Wadim
The product sides of the Rogers--Ramanujan identities and alike often appear to be "transparently modular" (functions). The old work by Rogers (1894) and recent work by Rosengren make use (somewhat implicitly) of this fact for proving the identities
Externí odkaz:
http://arxiv.org/abs/2411.11100
Autor:
Das, Sourabhashis
For a natural number n, let M(n) denote the maximum exponent of any prime power dividing n, and let m(n) denote the minimum exponent of any prime power dividing n. We study the second moments of these arithmetic functions and establish their limiting
Externí odkaz:
http://arxiv.org/abs/2411.08799
Autor:
Fan, Steve, Pollack, Paul
For an atomic domain $D$, the $elasticity$ $\rho(D)$ of $D$ is defined as $\sup\{r/s: \pi_1\cdots \pi_r = \rho_1 \cdots \rho_s,~ \text{where each $\pi_i, \rho_j$ is irreducible}\}$; the elasticity provides a concrete measure of the failure of unique
Externí odkaz:
http://arxiv.org/abs/2411.09063