A. Dixit

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math.NT2022

An effective bound on Generalized Diophantine m-tuples

S. Bhattacharjee, A. B. Dixit, D. Saikia

For non-zero integers $n$ and $k \geq 2$ , a generalized Diophantine $m$ -tuple with property $D_{k} (n)$ is a set of $m$ positive integers $S = {a_{1}, a_{2}, \dots, a_{m}}$ such that $a_ia_j…

math.NT2019

On Euler-Kronecker constants and the generalized Brauer-Siegel conjecture

Anup B. Dixit

As a natural generalization of the Euler-Mascheroni constant $γ$ , Y. Ihara introduced the Euler-Kronecker constant $γ_{K}$ attached to any number field $K$ . In this paper, we prove t…

math.NT2019

On the generalized Brauer-Siegel theorem for asymptotically exact families with solvable Galois closure

Anup B. Dixit

In 2002, M. A. Tsfasman and S. G. Vlăduţ formulated the generalized Brauer-Siegel conjecture for asymptotically exact families of number fields. In this article, we establish this…

math.NT2019

A uniqueness property of general Dirichlet series

Anup B. Dixit

Let $F (s) = \sum_{n} a_{n} / λ_{n}^{s}$ be a general Dirichlet series which is absolutely convergent on $ℜ (s) > 1$ . Assume that $F (s)$ has an analytic continuation and satisfies a growth condi…

math.NT2019

Large values of $L$ -functions on $1$ -line

Anup B. Dixit, Kamalakshya Mahatab

In this paper, we study lower bounds of a general family of $L$ -functions on the $1$ -line. More precisely, we show that for any $F (s)$ in this family, there exists arbitrary large…

An effective bound on Generalized Diophantine m-tuples

On Euler-Kronecker constants and the generalized Brauer-Siegel conjecture

On the generalized Brauer-Siegel theorem for asymptotically exact families with solvable Galois closure

A uniqueness property of general Dirichlet series

Large values of L-functions on 1-line

Large values of $L$ -functions on $1$ -line