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pro vyhledávání: '"Sedunova, Alisa"'
The Euler--Kronecker constant of a number field $K$ is the ratio of the constant and the residue of the Laurent series of the Dedekind zeta function $\zeta_K(s)$ at $s=1$. We study the distribution of the Euler--Kronecker constant $\gamma_q^+$ of the
Externí odkaz:
http://arxiv.org/abs/2407.09113
Kummer's conjecture predicts the asymptotic growth of the relative class number of prime cyclotomic fields. We substantially improve the known bounds of Kummer's ratio under three scenarios: no Siegel zero, presence of Siegel zero and assuming the Ri
Externí odkaz:
http://arxiv.org/abs/2402.13829
We will show that the number of integers $\leq x$ that can be written as the square of an integer plus the square of a prime equals $\frac{\pi}{2} \cdot \frac {x}{\log x}$ minus a secondary term of size $x/(\log x)^{ 1+\delta+o(1)}$, where $\delta :=
Externí odkaz:
http://arxiv.org/abs/2308.14911
When restricted to some non-negative multiplicative function, say f, bounded on primes and that vanishes on non square-free integers, our result provides us with an asymptotic for $\sum_{n \le X}f(n)/n$ with error term $O((\log X)^{\kappa-h-1+\vareps
Externí odkaz:
http://arxiv.org/abs/2201.08076
Autor:
Sedunova, Alisa
The number of solutions to $a^2+b^2=c^2+d^2 \le x$ in integers is a well-known result, while if one restricts all the variables to primes Erdos showed that only the diagonal solutions, namely, the ones with $\{a,b\}=\{c,d\}$ contribute to the main te
Externí odkaz:
http://arxiv.org/abs/2107.05525
Let $\zeta_q$ be a primitive $q^{\text{th}}$ root of unity with $q$ an arbitrary odd prime. The ratio of Kummer's first factor of the class number of the cyclotomic number field $\mathbb{Q}(\zeta_q)$ and its expected order of magnitude (a simple func
Externí odkaz:
http://arxiv.org/abs/1908.01152
Autor:
Sedunova, Alisa
E. Bombieri et J. Pila ont introduit une méthode qui donne les bornees sur le nombre de points entiers qui sont appartiennent d'un arc donné (sous les plusieurs hypothèses).Dans la partie algébrique nous généralisons la méthode de Bombieri Pil
Externí odkaz:
http://www.theses.fr/2017SACLS178/document
Akademický článek
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We give an informal survey of the historical development of computations related to prime number distribution and zeros of the Riemann zeta function.
Externí odkaz:
http://arxiv.org/abs/1810.05244
Publikováno v:
J. Number Theory 209 (2020), 147-166
The Jordan totient $J_k(n)$ can be defined by $J_k(n)=n^k\prod_{p\mid n}(1-p^{-k})$. In this paper, we study the average behavior of fractions $P/Q$ of two products $P$ and $Q$ of Jordan totients, which we call Jordan totient quotients. To this end,
Externí odkaz:
http://arxiv.org/abs/1810.04742