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Permanent URI for this collectionhttp://164.52.219.250:4000/handle/10263/7618

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    Second Moment of Degree Three L-Functions
    (ISI, 2025-04-23) Pal, Sampurna
    Let F be a Hecke-Maaß cusp form for SL(3, Z). In this dissertation, we obtain a nontrivial upper bound of the second moment of L(F, s) in the t-aspect:Z 2TT|L(F, 1/2 + it)|2dt ≪F,ϵ T3/2−3/32+ϵ. Immediate corollaries include improvements over the existing results on the Subconvexity bound for self-dual GL(3) L-functions in the t-aspect and for self-dual GL(3) × GL(2) Lfunctions in the GL(2) spectral aspect, the error term in the Rankin-Selberg problem, and the zero density estimate for GL(3) L-functions.
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    Environmental Degradations in Images: Analysis, Restoration, and Applications
    (Indian Statistical Institute, Kolkata, 2026-01-13) Bhandari, Harsh
    This thesis investigates computational models and methodologies for restoring images degraded by challenging environmental conditions such as haze and underwater environments. It further explores the analysis and estimation of particulate matter (PM) concentration from both day and night scenes under varying weather conditions, using degraded visual data as a primary input. Each environment introduces distinct forms of visual degradation, making image restoration a critical challenge that directly impacts applications including visibility enhancement, weather analysis, particulate concentration estimation, and object detection. By addressing these challenges, this thesis aims to develop adaptable, data-driven solutions that enhance image clarity and improve information extraction across diverse environmental scenarios, thereby enabling more accurate interpretation and utilization of visual data.