Zobrazeno 1 - 10
of 73
pro vyhledávání: '"Dutta, Parikshit"'
We compute the second moment of the Riemann zeta function for shifted arguments over a domain that extends the ones in the literature. We use the Riemann-Siegel formula for the error term in the approximate functional equation and take the products o
Externí odkaz:
http://arxiv.org/abs/2408.04247
We study the Weyl formula for the asymptotic number of eigenvalues of the Laplace-Beltrami operator with Dirichlet boundary condition on a Riemannian manifold in the context of geometric flows. Assuming the eigenvalues to be the energies of some asso
Externí odkaz:
http://arxiv.org/abs/2312.09777
Autor:
Dutta, Parikshit, Ghoshal, Debashis
The distribution of the non-trivial zeroes of the Riemann zeta function, according to the Riemann hypothesis, is tantalisingly similar to the zeroes of the partition functions (Fisher and Yang-Lee zeroes) of statistical mechanical models studied by p
Externí odkaz:
http://arxiv.org/abs/2102.13445
Autor:
Dutta, Parikshit, Ghoshal, Debashis
We propose to associate to a modular form (an infinite number of) complex valued functions on the $p$-adic numbers $\mathbb{Q}_p$ for each prime $p$. We elaborate on the correspondence and study its consequence in terms of the Mellin transforms and t
Externí odkaz:
http://arxiv.org/abs/2103.02443
Autor:
Dutta, Parikshit, Ghoshal, Debashis
We define a family of pseudodifferential operators on the Hilbert space $L^2(\mathbf{Q}_p)$ of complex valued square-integrable functions on the $p$-adic number field $\mathbf{Q}_p$. The Riemann zeta-function and the related Dirichlet $L$-functions c
Externí odkaz:
http://arxiv.org/abs/2003.00901
We propose the construction of an ensemble of unitary random matrices (UMM) for the Riemann zeta function. Our approach to this problem is `$p$-iecemeal', in the sense that we consider each factor in the Euler product representation of the zeta funct
Externí odkaz:
http://arxiv.org/abs/1807.07342
Wavelet analysis has been extended to the $p$-adic line $\mathbb{Q}_p$. The $p$-adic wavelets are complex valued functions with compact support. As in the case of real wavelets, the construction of the basis functions is recursive, employing scaling
Externí odkaz:
http://arxiv.org/abs/1804.00958
We explicitly find representations for different large $N$ phases of Chern-Simons matter theory on $S^2\times S^1$. These representations are characterised by Young diagrams. We show that no-gap and lower-gap phase of Chern-Simons-matter theory corre
Externí odkaz:
http://arxiv.org/abs/1801.07901
We show that large $N$ phases of a $0$ dimensional generic unitary matrix model (UMM) can be described in terms of topologies of two dimensional droplets on a plane spanned by eigenvalue and number of boxes in Young diagram. Information about differe
Externí odkaz:
http://arxiv.org/abs/1708.03298
There is a renewed interest in conformal field theories (CFT) on ultrametric spaces (p-adic field and its algebraic extensions) in view of their natural adaptability in the holographic setting. We compute the contributions from the exchange interacti
Externí odkaz:
http://arxiv.org/abs/1705.05678