H. Mousavi

activity

20162022

most citedS-Noetherian generalized power series rings

1 citations · 2 across the 7 of their papers we have counts for

collaborators

8 papers

math.NT2022

On a conjecture of Graham on the p-divisibility of central binomial coefficients

Ernie Croot, Hamed Mousavi, Maxie Schmidt

We show that for every $r \geq 1$ , and all $r$ distinct (sufficiently large) primes $p_{1}, ..., p_{r} > p_{0} (r)$ , there exist infinitely many integers $n$ such that $(n 2 n)$ is…

math.CA2021

Improving and Maximal Inequalities for Primes in Progressions

Christina Giannitsi, Michael T. Lacey, Hamed Mousavi +1

Assume that $y < N$ are integers, and that $(b, y) = 1$ . Define an average along the primes in a progression of diameter $y$ , given by integer $(b, y) = 1$ . \begin{align*} A_{N,y,b…

math.NT2021

Endpoint $ℓ^{r}$ improving estimates for Prime averages

Michael T. Lacey, Hamed Mousavi, Yaghoub Rahimi

Let $Λ$ denote von Mangoldt's function, and consider the averages \begin{align*} A_N f (x) &=\frac{1}{N}\sum_{1\leq n \leq N}f(x-n)Λ(n) . \end{align*} We prove sharp $ℓ^{p}$ -…

math.RA2020

On Reduced archimedean skew power series rings

Hamed Mousavi, Farzad Padashnik, Ayesha Asloob Qureshi

In this paper, we prove that if $R$ is an Archimedean reduced ring and satisfy ACC on annihilators, then $R [[x]]$ is also an Archimedean reduced ring. More generally we prove that…

math.NT2019

On a Class of Sums with Unexpectedly High Cancellation, and its Applications

Ernie Croot, Hamed Mousavi

Following attempts at an analytic proof of the Pentagonal Number Theorem, we report on the discovery of a general principle leading to an unexpected cancellation of oscillating sum…

math.NT2018

Factorization Theorems for Relatively Prime Divisor Sums, GCD Sums and Generalized Ramanujan Sums

Hamed Mousavi, Maxie D. Schmidt

We generalize recent matrix-based factorization theorems for Lambert series generating functions generating the coefficients $(f * 1) (n)$ for some arithmetic function $f$ . Our n…

math.RA2016★ 1 cited

S-Noetherian generalized power series rings

F. Padashnik, A. Moussavi, H. Mousavi

Let R be a ring with identity, (M;\leq) a commutative positive strictly ordered monoid and w_m an automorphism for each m \in M . The skew generalized power series ring R[[M,w]] is…