Bruce C. Berndt

University of Illinois Urbana-Champaign — United States

Mathematics · Physical Sciences

40h-index11.5kcitations551works0.82yr avg
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Research Topics

Advanced Mathematical Identities(382), Analytic Number Theory Research(349), Advanced Combinatorial Mathematics(117), History and Theory of Mathematics(78), Mathematical functions and polynomials(76)

Publications551 total

Sums of two squares and the tau-function: Ramanujan’s trail
Expositiones Mathematicae·2025· 2 citedOpen Access
Correction: Cubic and quintic analogues of Ramanujan’s septic theta function identity
The Ramanujan Journal·2025Open Access
Correction: Cubic and quintic analogues of Ramanujan’s septic theta function identity
The Ramanujan Journal·2025Open Access
Cubic and quintic analogues of Ramanujan’s septic theta function identity
The Ramanujan Journal·2025Open Access
An Arithmetic Sum Associated with the Classical Theta Function
arXiv (Cornell University)·2024Open Access
Sums of two squares and the tau-function: Ramanujan's trail
arXiv (Cornell University)·2024Open Access
Evaluations and relations for finite trigonometric sums
Research in the Mathematical Sciences·2024· 4 cited
Evaluations and relations for finite trigonometric sums
arXiv (Cornell University)·2024Open Access
Cubic and quintic analogues of Ramanujan's septic theta function identity
arXiv (Cornell University)·2023Open Access
Partitions with multiplicities associated with divisor functions
Journal of Mathematical Analysis and Applications·2023· 4 cited
Exact evaluations and reciprocity theorems for finite trigonometric sums
Research in the Mathematical Sciences·2023· 2 cited
Finite trigonometric sums arising from Ramanujan’s theta functions
The Ramanujan Journal·2023· 5 cited
Proofs of McIntosh's conjecture on Franel integrals and two generalizations
Advances in Mathematics·2023
Number Theory for the Millennium III
2023· 1 cited
Modified Bessel Functions in Analytic Number Theory
arXiv (Cornell University)·2023Open Access
Proofs of McIntosh's Conjecture on Franel Integrals and Two Generalizations
arXiv (Cornell University)·2022Open Access
Two general series identities involving modified Bessel functions and a class of arithmetical functions
Canadian Journal of Mathematics·2022· 4 cited
Finite trigonometric sums arising from Ramanujan's theta functions
arXiv (Cornell University)·2022Open Access
Exact evaluations and reciprocity theorems for finite trigonometric sums
arXiv (Cornell University)·2022· 1 citedOpen Access
A class of identities associated with Dirichlet series satisfying Hecke’s functional equation
Proceedings of the American Mathematical Society·2022· 10 cited
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Frequent Co-authors

George E. Andrews(7), Nayandeep Deka Baruah(5), Ronald J. Evans(4), Heng Huat Chan(4), Frank Garvan(2), Kenneth S. Williams(1), Jonathan M. Borwein(1), Peter Borwein(1), Richard A. Brualdi(1), Saurabh Bhargava(1), R. Rankin(1), Gert Almkvist(1), Chandrashekar Adiga(1), S. Bhargava(1), G. N. Watson(1), Boon Pin Yeap(1), Ken Ono(1), S. Bhargava(1), Lisa Jacobsen(1), Robert L. Lamphere(1)