Modular Forms and Related Topics in Number Theory

BERNHARD HEIM is Dean of Faculty of Science and Head of the Department Mathematics and Science, German University of Technology, Oman. He received his Ph.D. degree from the University of Mannheim, Germany, and was a postdoc at the Max Planck Institute for Mathematics, Bonn, Germany.B. RAMAKRISHNAN is Professor at the Department of Statistics and Applied Mathematics, Central University of Tamil Nadu, and is on lien from the Harish-Chandra Research Institute (HRI), Prayagraj, India. He completed his Ph.D. from Ramakrishna Mission Vivekananda College, Chennai, under the supervision of Prof. T.C. Vasudevan. He joined HRI (formerly known as Mehta Research Institute), Prayagraj, in April 1993. Earlier, he served HRI as Dean of Administration (2005–2009) and Dean of Academics (2015–2018). He was also Treasurer of the National Academy of Sciences, Prayagraj, from 2016–2019. His areas of research are automorphic forms, theory of modular forms of integral and half-integral weights, higher degree modular forms, Jacobi forms, and so on. Professor Ramakrishnan has guided several Ph.D. students, and his research papers have been published in several international journals of repute.BRUNDABAN SAHU is Associate Professor at the School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar, India. He completed his Ph.D. in Mathematics from the Harish-Chandra Research Institute in 2008 with the thesis titled “Some Problems in Number Theory” under Prof. B. Ramakrishnan. He was postdoctoral fellow at the Science Foundation of Ireland (SFI), University College Dublin, during November 2008–October 2010, under Prof. Dr. Robert Osburn. His areas of research include number theory, modular forms, and Jacobi forms. Dr. Sahu’s research papers have been published in various journals of repute.

• V. K. Adersh, On vanishing of Hecke operators.- S. D. Adhikari, B. Roy, and S. Sarkar, On a polynomial method of Rónyai in the study of zero-sum theorems.- B. Balasubramanyam, E. Ghate and R. Vangala, p-adic Asai L-functions attached to Bianchi cusp forms.- S. Böcherer, Arithmetic properties of vector-valued Siegel modular forms.- S. Das, Omega results for Fourier coefficients of half-integral weight and Siegel modular forms.- A. Hauffe-Waschbusch and A. Krieg, On Hecke theory for Hermitian modular forms.- B. Heim and M. Neuhauser, Sign Changes of the Ramanujan τ-function.- A. Kar and M. Ram Murty, The Central Limit Theorem in Algebra and Number Theory.- A. Kumar and J. Meher, Rankin-Cohen brackets and identities among eigenforms II.- M. Kumari and B. Sahu, Rankin-Cohen type operators for Hilbert-Jacobi forms.- M. K. Pandey and B. Ramakrishnan, Determining modular forms of half-integral weight by central values of convolution L-functions.- B. Ramakrishnan, B. Sahu and A. K. Singh, On the number of representations of a natural number by certain quaternary quadratic forms.- V. P. Ramesh, M. Makeshwari, M. Prithvi and R. Thatchaayini, Identities from Partition of the Symmetric group Sn.- M. M. Sreejith, A certain kernel function for L-values of half-integral weight Hecke eigenforms.- S. Kotyada and S. Muthukrishnan, On admissible set of primes in real quadratic fields.s.