Results 231 to 240 of about 37,887 (268)

Learning and embodied decisions in active inference

Priorelli M, Stoianov IP, Pezzulo G.
europepmc   +1 more source

Some of the next articles are maybe not open access.

Related searches:

ON DIRICHLET CHARACTERS OF POLYNOMIAL

Bulletin of the London Mathematical Society, 2002
The classical result, due to Pólya and Vinogradov, is that the estimates \[ \sum_{n=N+1}^{N+H}\chi(n)\ll q^{1/2}\log q \] holds for all nonprincipal Dirichlet characters \(\chi\) modulo \(q\). The main result of the note under review is to show that for certain primitive characters \(\chi\) modulo \(q\) and some special polynomials \(f(x)\) with ...
Zhang, Wenpeng, Yi, Yuan
openaire   +1 more source

On primitivity of Dirichlet characters

International Journal of Number Theory, 2015
Recall that a Dirichlet character is called imprimitive if it is induced from a character of smaller level, and otherwise it is called primitive. In this paper, we introduce a modification of "inducing to higher level" which causes imprimitive characters to behave primitively, in the sense that the properties of the associated Gauss sum and the ...
Daileda, R., Jones, N.
openaire   +1 more source

Dirichlet character sums

Acta Arithmetica, 1999
Let \(\chi\) be a Dirichlet character of conductor \(p^n\) with \(p \in {\mathbb{P}}\), \(n \in {\mathbb{N}}\), and let \(f(x) = a_0 + a_1 x + \cdots + a_k x^k\) be an integral polynomial such that \(k>3\) and \((p^n,a_1,\ldots,a_k)= p^m\). Using a special iteration the author proves some general character sum estimates of type \[ p^{-(n-m)(1-1/k ...
openaire   +2 more sources

Signatures of Dirichlet characters and elliptic curves

Journal of Number Theory, 2021
The authors study on signatures of the Dirichlet characters associated with elliptic curves. They find a lower bound for the number of conductors $q\leq Q$ with $q\equiv 1\pmod n$ having $k$ prime divisors of the Dirichlet characters $\chi$ of fixed order $n$ and with given values $\chi(m)$ for primes $m\leq b$. They introduce an elliptic curve variant
Dąbrowski, Andrzej, Pomykała, Jacek
openaire   +2 more sources

On Dirichlet Characters of Polynomials

Proceedings of the London Mathematical Society, 1963
Let \(q\) be a fixed positive integer and \(f(x)\) a nonlinear product of rational linear polynomials which is not a perfect \(q\)-th power. Let \(A\ll B\) mean \(A < k\vert B\vert\) for some positive constant \(k\). Theorem 1. For \(\varepsilon > 0\) if \(p\equiv 1\pmod q\) is a sufficiently large prime and \(\chi\) is a \(q\)-th order character ...
openaire   +1 more source

Sums with convolutions of Dirichlet characters

manuscripta mathematica, 2010
Let \(\chi_1\) and \(\chi_2\) be primitive Dirichlet characters with conductors \(q_1\) and \(q_2\), respectively, and let \[ S_{\chi_1,\chi_2}(X):=\sum_{ab\leq X}\chi_1(a)\chi_2(b). \] The authors prove that if \(X\geq q_2^{\frac 23}\geq q_1^{\frac 23}\) and \(\log X=q_2^{o(1)}\), then \[ \left| S_{\chi_1,\chi_2}(X)\right|\leq X^{\frac {13}{18}}q_1 ...
Banks, William D., Shparlinski, Igor E.
openaire   +2 more sources

Mean value of real Dirichlet characters using a double Dirichlet series

Canadian Mathematical Bulletin, 2023
AbstractWe study the double character sum $\sum \limits _{\substack {m\leq X,\\m\mathrm {\ odd}}}\sum \limits _{\substack {n\leq Y,\\n\mathrm {\ odd}}}\left (\frac {m}{n}\right )$ and its smoothly weighted counterpart. An asymptotic formula with power saving error term was obtained by Conrey, Farmer, and Soundararajan by applying the Poisson ...
openaire   +2 more sources

-Adic Dirichlet characters of algebraic function fields

Journal of Soviet Mathematics, 1979
A theory of precyclic P-extensions is developed which contains the well-known Witt theory. This theory makes it possible to describe so-called P-adic Dirichlet characters of function fields. In particular, for a trigonometric sum of the form where P is a prime number and f is a polynomial, its expression in terms of the zeros of a certain L function
openaire   +2 more sources

Menon-type identities concerning Dirichlet characters

2017
8 ...
openaire   +1 more source