First, I would like to express my heartfelt gratitude to my academic advisor, Professor Dr. Sujatha Ramdorai, for her invaluable guidance and encouragement throughout my graduate studies. Her mentorship and support were instrumental in the completion of this thesis. I would also like to thank Professor Cornelius Greither for his willingness to review an early draft of my work and for his suggestion that local class field theory could be applied to improve my results. This suggestion was critical in shaping the final form of this thesis.
I’m grateful to the professors with whom I have taken courses and participated in research projects at UBC. I feel especially indebted to Professors Malabika Pramanik, Lior Silberman, and Greg Martin. They have taught me so much, not only about mathematics but also about life. They have been a constant source of inspiration and encouragement throughout my time at UBC. The beautiful campus and excellent Faculty have provided an ideal environment for my research.
I would like to express my heartfelt gratitude to my high school mathematics teacher, famous as ASG sir in my hometown. Through his encouragement and guidance, I chose to pursue mathematics over physics, a decision I have never regretted. I am forever indebted to him for setting me on the path that led me to where I am today.
I lack the vocabulary in any language to express my heartfelt gratitude to my parents, especially my mother. She has been my guiding light throughout my life, from kindergarten to the end of high school, and has been actively involved in my studies. She is the reason for who I am and where I am today.
