5 papers
Cyclotomic norm congruences for zeta values and modular -values
Shubhrajit Bhattacharya, Anwesh Ray, R. Sujatha
We study congruences between special values of zeta functions and modular -functions in cyclotomic towers. The underlying mechanism is an integral norm congruence for finite-lev…
Congruent copies of finite patterns in planar point sets
Shubhrajit Bhattacharya, Ritesh Goenka
Given a finite nonempty planar point set , what is the maximum number of congruent copies of contained in a set of points in the Euclidean plane? Building on OpenAI's re…
QEDBENCH: Quantifying the Alignment Gap in Automated Evaluation of University-Level Mathematical Proofs
Santiago Gonzalez, Alireza Amiri Bavandpour, Peter Ye +48
As Large Language Models (LLMs) saturate elementary benchmarks, the research frontier has shifted from generation to the reliability of automated evaluation. We demonstrate that st…
Correlations of error terms for weighted prime counting functions
Shubhrajit Bhattacharya, Greg Martin, Reginald M. Simpson
Standard prime-number counting functions, such as , , and , have error terms with limiting logarithmic distributions once suitably normalized. The same is true of…
On monic abelian trace-one cubic polynomials
Shubhrajit Bhattacharya, Andrew O'Desky
We compute the asymptotic number of monic trace-one integral polynomials with Galois group and bounded height. For such polynomials we compute a height function coming from t…