Zobrazeno 1 - 10
of 29
pro vyhledávání: '"Purkait, Soma"'
Autor:
Dimabayao, Jerome T., Purkait, Soma
A positive integer $n$ is called a $\theta$-congruent number if there is a triangle with sides $a,b$ and $c$ for which the angle between $a$ and $b$ is equal to $\theta$ and its area is $n\sqrt{r^2 - s^2}$, where $0 < \theta < \pi$, $\cos \theta = s/
Externí odkaz:
http://arxiv.org/abs/2308.14381
Akademický článek
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Autor:
Baruch, Ehud Moshe, Purkait, Soma
We compute generators and relations for a certain $2$-adic Hecke algebra of level $8$ associated with the double cover of $\mathrm{SL}_2$ and a $2$-adic Hecke algebra of level $4$ associated with $\mathrm{PGL}_2$. We show that these two Hecke algebra
Externí odkaz:
http://arxiv.org/abs/1808.05526
Autor:
Baruch, Ehud Moshe, Purkait, Soma
Publikováno v:
Can. J. Math.-J. Can. Math. 72 (2020) 326-372
We define a subspace of the space of holomorphic modular forms of weight $k+1/2$ and level $4M$ where $M$ is odd and square-free. We show that this subspace is isomorphic under the Shimura-Niwa correspondence to the space of newforms of weight $2k$ a
Externí odkaz:
http://arxiv.org/abs/1609.06481
Autor:
Purkait, Soma
Let k be an odd integer and N a positive integer such that 4 | N. Let X be a Dirichlet character modulo N. Shimura decomposes the space of half-integral weight forms Sk/2(N,X) as Sk/2(N,X) = S0(N,X)oOΦSk/2(N,X,Φ) where Φ runs through the newforms
Externí odkaz:
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.560391
Autor:
Baruch, Ehud Moshe, Purkait, Soma
We characterize the space of new forms for $\Gamma_0(m)$ as a common eigenspace of certain Hecke operators which depend on primes $p$ dividing the level $m$. To do that we find generators and relations for a $p$-adic Hecke algebra of functions on $K=
Externí odkaz:
http://arxiv.org/abs/1503.02767
Autor:
Kumar, Narasimha, Purkait, Soma
Publikováno v:
Arch. Math. (Basel) 102 (2014), no. 4, 369-378
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 them. We also give a necessary and sufficient condition for a half-integr
Externí odkaz:
http://arxiv.org/abs/1304.6586
Autor:
Purkait, Soma
Publikováno v:
LMS J. Comput. Math. 16 (2013) 216-245
For a given cusp form $\phi$ of even integral weight satisfying certain hypotheses, Waldspurger's Theorem relates the critical value of the $\mathrm{L}$-function of the $n$-th quadratic twist of $\phi$ to the $n$-th coefficient of a certain modular f
Externí odkaz:
http://arxiv.org/abs/1208.4329
Autor:
Purkait, Soma
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. For modular forms of integral weight, Sturm's bounds give generators
Externí odkaz:
http://arxiv.org/abs/1208.4326
Autor:
Purkait, Soma
Publikováno v:
International Journal of Number Theory Vol. 9, No. 6 (2013)
Let $k$ be an odd integer $\ge 3$ and $N$ a positive integer such that $4 \mid N$. Let $\chi$ be an even Dirichlet character modulo $N$. Shimura decomposes the space of half-integral weight cusp forms $S_{k/2}(N,\chi)$ as a direct sum of $S_0(N,\chi)
Externí odkaz:
http://arxiv.org/abs/1205.7086