S. Purkait

activity

20122026

most citedOn Shimura's decomposition

8 citations · 23 across the 9 of their papers we have counts for

collaborators

9 papers

math.NT2026

Hecke Subalgebras and Local Newforms for the Metaplectic Double Cover of $SL_{2} (Q_{p})$

Ehud Moshe Baruch, Markos Karameris, Soma Purkait

Let $p$ be an odd prime, and let $SL_{2} (Z_{p})$ and $K_{0} (p^{n})$ denote the inverse images of $SL_{2} (Z_{p})$ and the congruence su…

math.NT2023

A variant of the congruent number problem

Jerome T. Dimabayao, Soma Purkait

A positive integer $n$ is called a $θ$ -congruent number if there is a triangle with sides $a, b$ and $c$ for which the angle between $a$ and $b$ is equal to $θ$ and its area is $n\s…

math.NT2018

Newforms of half-integral weight: the minus space of S_{k+1/2}(Γ_0(8M))

Ehud Moshe Baruch, Soma Purkait

We compute generators and relations for a certain $2$ -adic Hecke algebra of level $8$ associated with the double cover of $SL_{2}$ and a $2$ -adic Hecke algebra of level $4$ …

math.NT2016★ 5 cited

Newforms of half-integral weight: the minus space counterpart

Ehud Moshe Baruch, Soma Purkait

We define a subspace of the space of holomorphic modular forms of weight $k + 1/2$ and level $4 M$ where $M$ is odd and square-free. We show that this subspace is isomorphic under the…

math.NT2015★ 1 cited

Hecke algebras, new vectors and new forms on $Γ_{0} (m)$

Ehud Moshe Baruch, Soma Purkait

We characterize the space of new forms for $Γ_{0} (m)$ as a common eigenspace of certain Hecke operators which depend on primes $p$ dividing the level $m$ . To do that we find generato…

math.NT2013★ 4 cited

A Note on the Fourier coefficients of half-integral weight modular forms

Narasimha Kumar, Soma Purkait

In this note, we show that the algebraicity of the Fourier coefficients of half-integral weight modular forms can be determined by checking the algebraicity of the first few of the…

math.NT2012★ 4 cited

Hecke operators in half-integral weight

Soma Purkait

In \cite{Shimura}, Shimura introduced modular forms of half-integral weight, their Hecke algebras and their relation to integral weight modular forms via the Shimura correspondence…

math.NT2012★ 1 cited

Explicit application of Waldspurger's Theorem

Soma Purkait

For a given cusp form $ϕ$ of even integral weight satisfying certain hypotheses, Waldspurger's Theorem relates the critical value of the $L$ -function of the $n$ -th quadrat…

math.NT2012★ 8 cited

On Shimura's decomposition

Soma Purkait

Let $k$ be an odd integer $\geq 3$ and $N$ a positive integer such that $4 ∣ N$ . Let $χ$ be an even Dirichlet character modulo $N$ . Shimura decomposes the space of half-integral…

Hecke Subalgebras and Local Newforms for the Metaplectic Double Cover of SL2​(Qp​)

A variant of the congruent number problem

Newforms of half-integral weight: the minus space of S_{k+1/2}(Γ_0(8M))

Newforms of half-integral weight: the minus space counterpart

Hecke algebras, new vectors and new forms on Γ0​(m)

A Note on the Fourier coefficients of half-integral weight modular forms

Hecke operators in half-integral weight

Explicit application of Waldspurger's Theorem

On Shimura's decomposition

Hecke Subalgebras and Local Newforms for the Metaplectic Double Cover of $SL_{2} (Q_{p})$

Hecke algebras, new vectors and new forms on $Γ_{0} (m)$