The average elliptic curve has few integral

Acknowledgements. First and foremost, I would like to thank my family. Of course I cannot put into words how much their support has meant to me. It was my sister who first taught me arithmetic during long car rides when I was very young, and, as is evidenced by this thesis, I still am just as excited about it all these years later. Next I would like to thank my advisor, Jacob Tsimerman, for teaching me a tremendous amount of mathematics and always having a healthy dose of skepticism when listening to my arguments. I am greatly indebted to him and Arul Shankar for coming up with such a fun problem. I don't know how they did it, but I am lucky they are so skilled. I would like to thank all my teachers, in mathematics, physics, computer science , from Harvard, high school, LISG, and otherwise, for teaching me patiently for all these years. In particular I would like to thank Prof.s Gaitsgory, Elkies, Gross, Miller, and Gallian for advising me during my time at Harvard, Williams, and Duluth. If it weren't for Prof. Gallian's constant encouragement I would have never even considered asking for a problem. Actually I really must thank all my professors at Harvard as well, but nobody wants to read a listing of the entire Harvard faculty in a senior thesis. Finally, I would like to thank my friends for being awesome. Obviously you guys know who you are. for helpful conversations related to work in this thesis. I would of course also like to thank Anirudha Balasubramanian for helpful conversations related to the Irwin-Hall distribution.[2]