Some Contributions to Number Theory and Beyond

A symposium on number theory was organized at the Indian Institute of Science Education and Research Pune from July 12 - 16, 2021 in honour of Professor M. V. Subbarao (May 4, 1921 – February 15, 2006) on his birth centenary. Due to travel restrictions imposed by the COVID-19 pandemic, this symposium was conducted online and had participation from speakers all across the globe. The editors of this volume are glad to present the Proceedings of this symposium to readers.It contains twelve chapters contributed by symposium speakers, and a personal reminiscence of Professor Subbarao.These articles encompass a wide variety of topics, including those to which Prof. Subbarao has made fundamental contributions, such as partition theory, and the characterization of additive and multiplicative functions. Chapters touch upon wider themes in number theory, such as summation formulas arising from a boundary value problem in heat conduction, parity results for the generalized divisor function, probabilistic limit theorems for the zeta function, infinite-rank Euclidean lattices, the density of visible lattice points, and a question of Baker in transcendental number theory. Finally, in resonance with one of the most challenging problems that the world has faced (and continues to face) in recent times, this volume also contains an article on modelling pandemics with applications to COVID-19.

Baskar Balasubramanyam is an Associate Professor of Mathematics at IISER Pune. His research interests lie in the fields of Hida families, Hilbert modular forms, special values of L-functions, p-adic L-functions and Galois representations. He received his PhD from Brandeis University in USA. Before joining IISER Pune, he held postdoctoral positions at the Ben-Gurion University of the Negev, and California Institute of Technology. In addition to the current proceedings under consideration, he has edited "p-adic aspects of modular forms", Proceedings of a workshop held at IISER Pune in June, 2014, published by World Scientific. Further details about his research publications are available at the following link:

Kaneenika Sinha is an Associate Professor of Mathematics at IISER Pune. She studies questions at the intersection of number theory and probability, mainly in the context of modular forms, elliptic curves and regular graphs. She received her Ph.D. from Queen's University in Canada. Before joining IISER Pune, she was a faculty member in the Department of Mathematics at IISER Kolkata.

Prior to that, she has held postdoctoral positions at University of Toronto (in the GANITA lab), University of Alberta (as a Pacific Institute of Mathematical Sciences postdoctoral fellow) and Simons Laufer Mathematical Sciences Institute (formerly, Mathematical Sciences Research Institute), Berkeley.

She is an author of the book, "An introduction to the circle method" (co-authored with M. Ram Murty), which has appeared in the Student Mathematical Library series of the American Mathematical Society (Volume 104).

Mathukumalli Vidyasagar is a leading control theorist and a Fellow of Royal Society. He is currently a Distinguished Professor in Electrical Engineering at IIT Hyderabad. Previously he was the Cecil & Ida Green (II) Chair of Systems Biology Science at the University of Texas at Dallas. Prior to that he was an executive vice-president at Tata Consultancy Services(TCS) where he headed the Advanced Technology Center. Earlier, he was the director of Centre for Artificial Intelligence and Robotics (CAIR), a DRDO defence lab in Bangalore.