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My area of research is Number theory. I am interested in the topics related to arithmetic and analytic properties of modular forms, their variants and generalizations. During my Ph.D., my research has focused on arithmetic properties of regularized inner products and Fourier coefficients of harmonic Maass forms.
Research Articles
Research Articles
(Under preparation) K. Bringmann, J-W. van-Ittersum , V. Kalia, B. V. Pandey , to be determined.
V. Kalia, B. Kumar, Arithmetic of regularized inner products and Rohrlich-Jensen type divisor sums for j-invariant, (2025), submitted.
V. Kalia, B. Kumar, Regularized inner products and modular invariants for real quadratic fields, (2024), submitted.
V. Kalia, B. Kumar, On traces of cycle integral attached to harmonic Maass forms, (2023), submitted.
V. Kalia, B. Kumar, Traces of Poincaré series at square discriminants and Fourier coefficients of mock modular forms, Acta Arith., 216 (2024), 1-18.
V. Kalia, On Interpretation of Fourier coefficients of Zagier type lifts, Arch. Math. (Basel), 123 (2024), 147-162.
Research talks
Research talks
"Traces of Poincaré series at square discriminants and Fourier coefficients of mock modular forms" at Harmonic Maass forms, mock modular forms & and their applications, ICTS, India, Jul 2025.
"Fourier coefficients of mock modular forms and their arithmetic", IIT Ropar, Feb 2025.
"On interpretation of Fourier coefficients of Zagier type lifts", IISER Bhopal, Nov 2024.
"Traces of Poincaré series at square discriminants and Fourier coefficients of mock modular forms", Building Bridges: 6th EU/US Summer School & Workshop on Automorphic Forms and Related Topics (BB6), CIRM, Marseille, France, Sep 2024.
Other activities
Other activities
Research visit at IISER Bhopal. Host: Dr. Karam Deo Shankhadhar, Jul 2025.
Reseacrh visit at University of Cologne. Host: Prof. Kathrin Bringmann, April 2025.
Best Oral Presentation award for a talk on “Fourier coefficients of mock modular forms and their arithmetic” at Cynosure-8.0 and NSAM 2025, IIT Ropar, Feb 2025.
Poster presentation titled “Traces and Fourier coefficients of mock modular forms” on the annual research day of the Department of Mathematics, Indian Institute of Technology Ropar, Feb 2024.
National Centre for Mathematics Workshop on “Analytic Methods in Algebraic Number Theory", Dec 2023.
National Centre for Mathematics Workshop on “Elliptic Curves", Apr 2023.
National Centre for Mathematics Workshop on “Jacobi Forms", Dec 2022.
Poster presentation titled “An insight into modular and mock modular forms” on the annual research day of the Department of Mathematics, Indian Institute of Technology Ropar, Dec 2022 .
National Centre for Mathematics Workshop on “Elliptic Curves, Elliptic Functions and Transcendence", Nov 2022.
Workshop on “Groups and Symmetry", Dec 2017 .
Mathematics Training and Talent Search Programme Internship, May 2017.
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