Naser T. Sardari

activity

20152026

most citedOptimal strong approximation for quadratic forms

19 citations · 40 across the 17 of their papers we have counts for

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18 papers · 1 filter

math.NT2024

New Lower Bounds for the Schur-Siegel-Smyth Trace Problem

Bryce Joseph Orloski, Naser Talebizadeh Sardari, Alexander Smith

We derive and implement a new way to find lower bounds on the smallest limiting trace-to-degree ratio of totally positive algebraic integers and improve the previously best known b…

math.NT2023

A quantitative converse of Fekete's theorem

Naser Talebizadeh Sardari, Bryce Joseph Orloski

Given a compact subset $Σ \subset R$ (or $C$ ) with logarithmic capacity greater than zero, we construct an explicit family of probability measures supported on $Σ$ …

math.NT2023

Limiting distributions of conjugate algebraic integers

Bryce Joseph Orloski, Naser Talebizadeh Sardari

Let $Σ \subset C$ be a compact subset of the complex plane, and $μ$ be a probability distribution on $Σ$ . We give necessary and sufficient conditions for $μ$ to be the weak…

math.NT2021

Intersecting geodesics on the modular surface

Junehyuk Jung, Naser Talebizadeh Sardari

We introduce the \textit{modular intersection kernel}, and we use it to study how geodesics intersect on the full modular surface $\mathbb{X}=PSL_2\left(\mathbb{Z}\right) \backslas…

math.NT2021★ 3 cited

Higher Fourier interpolation on the plane

Naser Talebizadeh Sardari

Let $l \geq 6$ be any integer, where $l \equiv 2$ mod $4$ . Suppose that $μ (τ) d τ$ is a measure with bounded variation and is supported on a compact subset of the complex plane, where…

math.NT2019

Ramanujan graphs and exponential sums over function fields

Naser T. Sardari, Masoud Zargar

We prove that $q + 1$ -regular Morgenstern Ramanujan graphs $X^{q, g}$ (depending on $g \in F_{q} [t]$ ) have diameter at most $\left(\frac{4}{3}+\varepsilon\right)\log_{q}|X^{q,g}|…

math.NT2019

Optimal strong approximation for quadrics over $F_{q} [t]$

Naser T. Sardari, Masoud Zargar

Suppose $q$ is a fixed odd prime power, $F (x)$ is a non-degenerate quadratic form over $F_{q} [t]$ of discriminant $Δ$ in $d \geq 5$ variables $x$ , and $f,g\in\mat…

math.NT2019★ 4 cited

The Siegel variance formula for quadratic forms

Naser T. Sardari

We introduce a smooth variance sum associated to a pair of positive definite symmetric integral matrices $A_{m \times m}$ and $B_{n \times n}$ , where $m \geq n$ . By using the oscillat…

math.NT2018

The diophantine exponent of the $Z / q Z$ points of $S^{d - 2} \subset S^{d}$

Mostafa W. Hassan, Yuchen Mao, Naser T. Sardari +2

Assume a polynomial-time algorithm for factoring integers, Conjecture~\ref{conj}, $d \geq 3,$ and $q$ and $p$ are prime numbers, where $p \leq q^{A}$ for some $A > 0$ . We develop a polyn…

math.NT2018★ 2 cited

Bounds on the multiplicity of the Hecke eigenvalues

Naser T. Sardari

Fix an integer $N$ and a prime $p ∤ N$ where $p \geq 5$ . We show that the number of newforms $f$ (up to a scalar multiple) of level $N$ and even weight $k$ such that $\mathcal{T}…

math.NT2018★ 2 cited

The least prime number represented by a binary quadratic form

Naser T. Sardari

Let $D < 0$ be a fundamental discriminant and $h (D)$ be the class number of $Q (D)$ . Let $R (X, D)$ be the number of classes of the binary quadratic forms of discriminan…

math.NT2018

The Cramér conjecture holds with a positive probability

Naser T. Sardari

We prove that a positive proportion of the intervals of any fixed scalar multiple of $lo g (X)$ in the dyadic interval $[X, 2 X]$ contain a prime number. We also show that a positive…

math.NT2018

The least prime ideal in a given ideal class

Naser T. Sardari

Let $K$ be a number field with the discriminant $D_{K}$ and the class number $h_{K}$ , which has bounded degree over $Q$ . By assuming GRH, we prove that every ideal class of…

math.NT2017★ 2 cited

Quantum Chaos on random Cayley graphs of $SL_{2} [Z / p Z]$

Igor Rivin, Naser T. Sardari

We investigate the statistical behavior of the eigenvalues and diameter of random Cayley graphs of $SL_{2} [Z / p Z]$ %and the Symmetric group $S_{n}$ as the prime…

math.NT2017★ 8 cited

Complexity of strong approximation on the sphere

Naser T Sardari

By assuming some widely-believed arithmetic conjectures, we show that the task of accepting a number that is representable as a sum of $d \geq 2$ squares subjected to given congruenc…

math.NT2016

Quadratic forms and semiclassical eigenfunction hypothesis for flat tori

Naser T Sardari

Let $Q (X)$ be any integral primitive positive definite quadratic form with discriminant $D$ and in $k$ variables where $k \geq 4$ . We give an upper bound on the number of integral so…

math.NT2015

Diameter of Ramanujan Graphs and Random Cayley Graphs

Naser T Sardari

We study the diameter of LPS Ramanujan graphs $X_{p, q}$ . We show that the diameter of the bipartite Ramanujan graphs is greater than $(4/3) lo g_{p} (n) + O (1)$ where $n$ is the numb…

math.NT2015★ 19 cited

Optimal strong approximation for quadratic forms

Naser T Sardari

For a non-degenerate integral quadratic form $F (x_{1}, \dots, x_{d})$ in $d \geq 5$ variables, we prove an optimal strong approximation theorem. Let $Ω$ be a fixed compact subset of the…

New Lower Bounds for the Schur-Siegel-Smyth Trace Problem

A quantitative converse of Fekete's theorem

Limiting distributions of conjugate algebraic integers

Intersecting geodesics on the modular surface

Higher Fourier interpolation on the plane

Ramanujan graphs and exponential sums over function fields

Optimal strong approximation for quadrics over Fq​[t]

The Siegel variance formula for quadratic forms

The diophantine exponent of the Z/qZ points of Sd−2⊂Sd

Bounds on the multiplicity of the Hecke eigenvalues

The least prime number represented by a binary quadratic form

The Cramér conjecture holds with a positive probability

The least prime ideal in a given ideal class

Quantum Chaos on random Cayley graphs of SL2​[Z/pZ]

Complexity of strong approximation on the sphere

Quadratic forms and semiclassical eigenfunction hypothesis for flat tori

Diameter of Ramanujan Graphs and Random Cayley Graphs

Optimal strong approximation for quadratic forms

Optimal strong approximation for quadrics over $F_{q} [t]$

The diophantine exponent of the $Z / q Z$ points of $S^{d - 2} \subset S^{d}$

Quantum Chaos on random Cayley graphs of $SL_{2} [Z / p Z]$