Anurag Sahay

Journal article Random Structures and Algorithms · August 1, 2026 For a random subset of a finite group (Formula presented.) of cardinality (Formula presented.), we consider the VC-dimension of the family of its translates (equivalently the VC-dimension of a random Cayley graph) and prove a law of large numbers as (Formu ... Full text Cite

The shifted convolution problem in function fields

Journal article Mathematische Annalen · May 1, 2026 We study the shifted convolution problem for the divisor function in function fields in the large degree limit, that is, the average value of d(f)d(f+h) where f runs over monic polynomials in Fq[T] of a given degree, and h is a given monic polynomial. We p ... Full text Cite

The fourth moment of the Hurwitz zeta function

Journal article Journal Fur Die Reine Und Angewandte Mathematik · January 1, 2025 We prove a sharp upper bound for the fourth moment of the Hurwitz zeta function ζ (s, α) on the critical line when the shift parameter α is irrational and of irrationality exponent strictly less than 3. As a consequence, we determine the order of magnitude ... Full text Cite

The VC dimension of quadratic residues in finite fields

Journal article Discrete Mathematics · January 1, 2025 We study the Vapnik–Chervonenkis (VC) dimension of the set of quadratic residues (i.e. squares) in finite fields, Fq, when considered as a subset of the additive group. We conjecture that as q→∞, the squares have the maximum possible VC-dimensio ... Full text Cite

PRINCIPAL EIGENVECTORS IN HYPERGRAPH TURÁN PROBLEMS

Journal article Electronic Journal of Linear Algebra · January 5, 2024 For a general class of hypergraph Turán problems with uniformity r, we investigate the principal eigenvector for the p-spectral radius (in the sense of Keevash–Lenz–Mubayi and Nikiforov) for the extremal graphs, showing in a strong sense that these eigenve ... Full text Cite

Moments of the Hurwitz zeta function on the critical line

Journal article Mathematical Proceedings of the Cambridge Philosophical Society · May 28, 2023 We study the moments {equation presented} of the Hurwitz zeta function ζ (s, α) on the critical line, s=1/2 + it with a rational shift α ∈ Q. We conjecture, in analogy with the Riemann zeta function, that {equation presented}. Using heuristics from analyti ... Full text Cite

A paucity problem associated with a shifted integer analogue of the divisor function

Journal article Journal of Number Theory · January 1, 2023 Suppose that θ is irrational. Then almost all elements ν∈Z[θ] that may be written as a k-fold product of the shifted integers n+θ (n∈N) are thus represented essentially uniquely. ... Full text Cite