Zobrazeno 1 - 10
of 144
pro vyhledávání: '"Gun, Sanoli"'
Autor:
Gun, Sanoli, Naik, Sunil
In this article, we investigate large prime factors of Fourier coefficients of non-CM normalized cuspidal Hecke eigenforms in short intervals. One of the new ingredients involves deriving an explicit version of Chebotarev density theorem in an interv
Externí odkaz:
http://arxiv.org/abs/2405.04698
Autor:
Gun, Sanoli, Lunia, Rashi
In a recent work arXiv:2004.14450, it has been shown that $L$-functions associated with arbitrary non-zero cusp forms take large values at the central critical point. The goal of this note is to derive analogous results for twists of Dirichlet-type f
Externí odkaz:
http://arxiv.org/abs/2405.02443
Autor:
Gun, Sanoli, Lunia, Rashi
Publikováno v:
Bulletin of the London Mathematical Society, vol. 56, 2024, 1570-1586
In 2008, Soundararajan showed that there exists a normalized Hecke eigenform $f$ of weight $k$ and level one such that $$ L(1/2, f ) ~\geq~ \exp\Bigg( (1 + o(1)) \sqrt{\frac{2\log k}{\log\log k} }\Bigg) $$ for sufficiently large $k \equiv 0 \pmod{4}$
Externí odkaz:
http://arxiv.org/abs/2405.02428
Autor:
Gun, Sanoli, Naik, Sunil L
Publikováno v:
Forum Mathematicum, vol. 36, no. 1, 2024, pp. 173-192
Let $\tau$ denote the Ramanujan tau function. One is interested in possible prime values of $\tau$ function. Since $\tau$ is multiplicative and $\tau(n)$ is odd if and only if $n$ is an odd square, we only need to consider $\tau(p^{2n})$ for primes $
Externí odkaz:
http://arxiv.org/abs/2402.07944
Publikováno v:
Mathematische Annalen, 2023
In this article, we investigate a non-Archimedean analogue of a question of Atkin and Serre. More precisely, we derive lower bounds for the largest prime factor of non-zero Fourier coefficients of non-CM normalized cuspidal Hecke eigenforms of even w
Externí odkaz:
http://arxiv.org/abs/2402.07943
Autor:
Gun, Sanoli, Naik, Sunil L
A well known result of Breulmann states that Hecke eigenvalues of Saito-Kurokawa lifts are positive. In this article, we show that the Hecke eigenvalues of an Ikeda lift at primes are positive. Further, we derive lower and upper bounds of these Hecke
Externí odkaz:
http://arxiv.org/abs/2402.06145
Autor:
Gun, Sanoli, Kandhil, Neelam
Publikováno v:
International Journal of Number Theory, 2022
It is an open question of Baker whether the numbers $L(1, \chi)$ for non-trivial Dirichlet characters $\chi$ with period $q$ are linearly independent over $\mathbb{Q}$. The best known result is due to Baker, Birch and Wirsing which affirms this when
Externí odkaz:
http://arxiv.org/abs/2212.00376
Publikováno v:
Journal of Number Theory, vol. 244, 2023, 63-83
The study of linear independence of $L(k, \chi)$ for a fixed integer $k>1$ and varying $\chi$ depends critically on the parity of $k$ vis-\`a-vis $\chi$. This has been investigated by a number of authors for Dirichlet characters $\chi$ of a fixed mod
Externí odkaz:
http://arxiv.org/abs/2212.00366
Publikováno v:
Journal of Number Theory, Volume 243, February 2023, Pages 13-37
Let $\mathbf{K}$ be a number field and $\mathfrak{q}$ an integral ideal in $\mathcal{O}_{\mathbf{K}}$. A result of Tatuzawa from 1973, computes the asymptotic (with an error term) for the number of ideals with norm at most $x$ in a class of the narro
Externí odkaz:
http://arxiv.org/abs/2208.06602
Pila and Tsimerman proved in 2017 that for every $k$ there exists at most finitely many $k$-tuples $(x_1,\ldots, x_k)$ of distinct non-zero singular moduli with the property "$x_1, \ldots,x_k$ are multiplicatively dependent, but any proper subset of
Externí odkaz:
http://arxiv.org/abs/2207.05183