P. Monsky

activity

20042017

most citedTight closure does not commute with localization

11 citations · 52 across the 18 of their papers we have counts for

collaborators

19 papers

math.NT2017

Generators and relations for the shallow mod 2 Hecke algebra in levels $Γ_{0} (3)$ and $Γ_{0} (5)$

Paul Monsky

Let $M (odd) \subset Z /2 [[x]]$ be the space of odd mod~2 modular forms of level $Γ_{0} (3)$ . It is known that the formal Hecke operators $T_{p} : Z /2 [[x]] \to Z /2 [[x]]$ ,…

math.NT2016

A characteristic 2 recurrence related to $U_{5}$ , with a Hecke algebra application

Paul Monsky

In arXiv:1603.03910 [math.NT] we introduced some $C_{n}$ in $Z /2 [t]$ defined by a linear recurrence and showed that each $C_{n}$ , $n \equiv 0 mod 4$ , is a sum of $C_{k}$ , $k < n$ .…

math.NT2016★ 3 cited

A Hecke algebra attached to mod 2 modular forms of level 5

Paul Monsky

Let $F$ be the element $\sum_{n odd, n > 0} x^{n^{2}}$ of $Z /2 [[x]]$ . Set $G = F (x^{5})$ , $D = F (x) + F (x^{25})$ . For $k > 0$ , $(k, 10) = 1$ , define $D_{k}$ as follows. $D_{1} = D$ , $D_…

math.NT2016★ 2 cited

Variations on a Lemma of Nicolas and Serre

Paul Monsky

The "Nicolas-Serre code", $(a, b) \leftrightarrow t^{n}$ , is a bijection between $N \times N$ and those $t^{n}$ , $n$ odd, in $Z /2 [t]$ . Suppose $A_{n}$ , $n$ odd, in $Z /2 [t]$ are defin…

math.NT2016★ 1 cited

A characteristic 2 recurrence related to $U_{3}$ , with a Hecke algebra application

Paul Monsky

I begin with a simple modular form motivated proof of the following: Let $C_{n}$ in $Z /2 [[t]]$ be defined by $C_{n + 4} = C_{n + 3} + (t^{4} + t^{3} + t^{2} + t) C_{n} + t^{n} (t^{2} + t)$ , with…

math.NT2015★ 5 cited

A Hecke algebra attached to mod 2 modular forms of level 3

Paul Monsky

Let $D$ in $Z /2 [[x]]$ be $\sum x^{n^{2}}$ , $n > 0$ and prime to $6$ . Let $W$ be spanned by the $D^{k}$ , $k > 0$ and prime to $6$ . Then the formal Hecke operators $T_{p}$ , $p > 3$ , stabil…

Generators and relations for the shallow mod 2 Hecke algebra in levels Γ0​(3) and Γ0​(5)

A characteristic 2 recurrence related to U5​, with a Hecke algebra application

A Hecke algebra attached to mod 2 modular forms of level 5

Variations on a Lemma of Nicolas and Serre

A characteristic 2 recurrence related to U3​, with a Hecke algebra application

A Hecke algebra attached to mod 2 modular forms of level 3

Generators and relations for the shallow mod 2 Hecke algebra in levels $Γ_{0} (3)$ and $Γ_{0} (5)$

A characteristic 2 recurrence related to $U_{5}$ , with a Hecke algebra application

A characteristic 2 recurrence related to $U_{3}$ , with a Hecke algebra application