Articles written in Proceedings – Mathematical Sciences
Volume 122 Issue 1 February 2012 pp 99-120
An 𝑛-Dimensional Pseudo-Differential Operator Involving the Hankel Transformation
R S Pathak Akhilesh Prasad Manish Kumar
An 𝑛-dimensional pseudo-differential operator (p.d.o.) involving the 𝑛-dimensional Hankel transformation is defined. The symbol class $H^m$ is introduced. It is shown that p.d.o.'s associated with symbols belonging to this class are continuous linear mappings of the 𝑛-dimensional Zemanian space $H_\mu(I^n)$ into itself. An integral representation for the p.d.o. is obtained. Using the Hankel convolution, it is shown that the p.d.o. satisfies a certain $L^1$-norm inequality.
Volume 129 Issue 3 June 2019 Article ID 0038 Research Article
Ramification theory and formal orbifolds in arbitrary dimension
Formal orbifolds are defined in higher dimension to study wild ramification. Their étale fundamental groups are also defined. It is shown that the fundamental groups of formal orbifolds have certain finiteness property and it is also shown that they can be used to approximate the étale fundamental groups of normal varieties. Étale site on formal orbifolds are also defined.This framework allows one to study wild ramification in an organized way. Brylinski–Kato filtration, Lefschetz theorem for fundamental groups and $l$-adic sheaves in these contexts are also studied.
Volume 130 All articles Published: 10 January 2020 Article ID 0002 Research Article
Signs of Fourier coefficients of cusp form at sumof two squares
SOUMYARUP BANERJEE MANISH KUMAR PANDEY
In this article,we investigate the sign changes of the sequence of coefficientsat sum of two squareswhere the coefficients are the Fourier coefficients of the normalized Hecke eigen cusp form for the full modular group.We provide the quantitative result for the number of sign changes of the sequence in a small interval.
Volume 133, 2023
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