Zobrazeno 1 - 10
of 626
pro vyhledávání: '"Washington, A. C."'
Let $K$ be an imaginary quadratic field in which the odd prime $p$ does not split. When the $p$-part of the class group of $K$ is cyclic, we describe the possible structures for the $p$-part of the class group of the first level of the cyclotomic $\m
Externí odkaz:
http://arxiv.org/abs/2410.06193
Deciding whether or not two polynomials have isomoprhic splitting fields over the rationals is the Field Isomorphism Problem. We consider polynomials of the form $f_n(x) = x^4-nx^3-6x^2+nx+1$ with $n \neq 3$ a positive integer and we let $K_n$ denote
Externí odkaz:
http://arxiv.org/abs/2406.10414
Autor:
Washington, Lawrence C.
For a real number $k$, define $\pi_k(x) = \sum_{p\le x} p^k$. When $k>0$, we prove that $$ \pi_k(x) - \pi(x^{k+1}) = \Omega_{\pm}\left(\frac{x^{\frac12+k}}{\log x} \log\log\log x\right) $$ as $x\to\infty$, and we prove a similar result when $-1
Externí odkaz:
http://arxiv.org/abs/2209.12845
This paper studies Iwasawa invariants in anti-cyclotomic towers. We do this by proposing two heuristics supported by computations. First we propose the Intersection Heuristics: these model `how often' the $p$-Hilbert class field of an imaginary quadr
Externí odkaz:
http://arxiv.org/abs/2207.13199
We adapt a known technique for searching for ideal classes of arbitrary order and then apply it to three families of number fields. We show that a family of cyclic sextic number fields has infinitely many fields in it that contain a relative ideal cl
Externí odkaz:
http://arxiv.org/abs/2206.12313
Autor:
Jonathan L M Fontes, Ricardo Khouri, Luis Gustavo C Reinaldo, Erina M A Hassegawa, Antônio José Meneses Filho, Caroline V B de Melo, Pablo Ivan P Ramos, Rafael de Deus Moura, Carla Pagliari, Marta Santos, Raimundo José C Araújo, Johan Van Weyenbergh, Luiz A R de Freitas, Carlos Henrique N Costa, Washington L C Dos-Santos
Publikováno v:
PLoS Neglected Tropical Diseases, Vol 18, Iss 6, p e0011877 (2024)
The spleen plays a pivotal role in the pathogenesis of visceral leishmaniasis. In severe forms of the disease, the spleen undergoes changes that can compromise its function in surveilling blood-circulating pathogens. In this study, we present an inte
Externí odkaz:
https://doaj.org/article/c547186499144f099ee4dda9bf45414b
Autor:
Jin, Steven, Washington, Lawrence C.
Let $E/\mathbb{Q}$ be an elliptic curve. For a prime $p$ of good reduction, let $r(E,p)$ be the smallest non-negative integer that gives the $x$-coordinate of a point of maximal order in the group $E(\mathbb{F}_p)$. We prove unconditionally that $r(E
Externí odkaz:
http://arxiv.org/abs/2104.13256
Autor:
Knospe, Heiko, Washington, Lawrence C.
We study $p$-adic $L$-functions $L_p(s,\chi)$ for Dirichlet characters $\chi$. We show that $L_p(s,\chi)$ has a Dirichlet series expansion for each regularization parameter $c$ that is prime to $p$ and the conductor of $\chi$. The expansion is proved
Externí odkaz:
http://arxiv.org/abs/2102.02851
Autor:
Kercia P. Cruz, Antonio L. O. A. Petersen, Marina F. Amorim, Alan G. S. F. Pinho, Luana C. Palma, Diana A. S. Dantas, Mariana R. G. Silveira, Carine S. A. Silva, Ana Luiza J. Cordeiro, Izabella G. Oliveira, Gabriella B. Pita, Bianca C. A. Souza, Gilberto C. Bomfim, Cláudia I. Brodskyn, Deborah B. M. Fraga, Isadora S. Lima, Maria B. R. de_Santana, Helena M. P. Teixeira, Juliana P. B. de_Menezes, Washington L. C. Santos, Patrícia S. T. Veras
Publikováno v:
Pathogens, Vol 13, Iss 8, p 630 (2024)
Background: Leishmaniasis is a significant global public health issue that is caused by parasites from Leishmania genus. With limited treatment options and rising drug resistance, there is a pressing need for new therapeutic approaches. Molecular cha
Externí odkaz:
https://doaj.org/article/68291c47a15b4e23ae429c6879a188ed
Publikováno v:
Monatshefte f\"ur Mathematik 195, no. 3 (2021), 489-496
We prove that every finite abelian group G occurs as a subgroup of the class group of infinitely many real cyclotomic fields.
Comment: This version corrects some small inaccuracies in the proof of Proposition 3
Comment: This version corrects some small inaccuracies in the proof of Proposition 3
Externí odkaz:
http://arxiv.org/abs/2011.07409