Some Contributions to Number Theory and Beyond

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.

• Preface.- Prof. Mathukumalli Venkata Subbarao: A Personal Reminiscence.- Results and conjectures related to the work of M.V. Subbarao.- Partition Identities for k-Regular Partitions with Distinct Parts.- Some reflections on the partition function.- On the number of parts in all partitions enumerated by the Rogers-Ramanujan identities.- Ramanujan and Koshliakov Meet Abel and Plana.- Infinite-rank Euclidean Lattices and Loop Groups.- Parity results concerning the generalized divisor function involving small prime factors of integers.- On a limit theorem for zeta functions.- On the density of visible lattice points along polynomials.- Around a question of Baker.- On quadratic factors of trinomials.- SUTRA: An Approach to Modelling Pandemics with Undetected Patients, and Applications to COVID-19.