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pro vyhledávání: '"Akhtari, Shabnam"'
In this expository article, we compare Malle's conjecture on counting number fields of bounded discriminant with recent conjectures of Ellenberg--Satriano--Zureick-Brown and Darda--Yasuda on counting points of bounded height on classifying stacks. We
Externí odkaz:
http://arxiv.org/abs/2402.10355
Let $K$ be an algebraic number field and $H$ the absolute Weil height. Write $c_K$ for a certain positive constant that is an invariant of $K$. We consider the question: does $K$ contain an algebraic integer $\alpha$ such that both $K = \mathbb{Q}(\a
Externí odkaz:
http://arxiv.org/abs/2307.11849
Autor:
Akhtari, Shabnam
Publikováno v:
Ess. Number Th. 1 (2022) 57-72
Some upper bounds for the number of monogenizations of quartic orders are established by considering certain classical Diophantine equations, namely index form equations in quartic number fields, and cubic and quartic Thue equations.
Comment: a
Comment: a
Externí odkaz:
http://arxiv.org/abs/2203.10235
Autor:
Akhtari, Shabnam, Vaaler, Jeffrey D.
We prove inequalities that compare the regulator of a number field with its absolute discriminant. We refine some ideas in Silverman's work in 1984 where such general inequalities are first proven. In order to prove our main theorems, we combine thes
Externí odkaz:
http://arxiv.org/abs/2112.15268
Autor:
AKHTARI, Shabnam, VAALER, Jeffrey D.
Publikováno v:
Journal de Théorie des Nombres de Bordeaux, 2023 Jan 01. 35(1), 259-282.
Externí odkaz:
https://www.jstor.org/stable/48728098
Autor:
Akhtari, Shabnam, Vaaler, Jeffrey D.
We generalize an inequality for the determinant of a real matrix proved by A. Schinzel, to more general exterior products of vectors in Euclidean space. We apply this inequality to the logarithmic embedding of $S$-units contained in a number field $k
Externí odkaz:
http://arxiv.org/abs/2009.10857
Autor:
Akhtari, Shabnam, Vaaler, Jeffery D.
We prove inequalities that compare the relative regulator of an extension of number fields with a product of heights of multiplicatively independent relative units.
Comment: This is an extension of results in Section 7 of the version 1. This art
Comment: This is an extension of results in Section 7 of the version 1. This art
Externí odkaz:
http://arxiv.org/abs/2008.06124
Autor:
Akhtari, Shabnam
For any fixed nonzero integer $h$, we show that a positive proportion of integral binary quartic forms $F$ do locally everywhere represent $h$, but do not globally represent $h$. We order classes of integral binary quartic forms by the two generators
Externí odkaz:
http://arxiv.org/abs/2002.00548
Autor:
Akhtari, Shabnam, Bengoechea, Paloma
Publikováno v:
Trans. Amer. Math. Soc. 374 (2021), 1687-1709
We will give new upper bounds for the number of solutions to the inequalities of the shape $|F(x , y)| \leq h$, where $F(x , y)$ is a sparse binary form, with integer coefficients, and $h$ is a sufficiently small integer in terms of the absolute valu
Externí odkaz:
http://arxiv.org/abs/1906.03705
Autor:
Akhtari, Shabnam, Vaaler, Jeffrey D.
We prove a new lower bound for the Mahler measure of a polynomial in one and in several variables that depends on the complex coefficients, and the number of monomials. In one variable our result generalizes a classical inequality of Mahler. In $M$ v
Externí odkaz:
http://arxiv.org/abs/1810.12413