Hrishabh Mishra
I am a second-year Master's student in Fundamental Mathematics at Université Paris Cité and a fellow of the Paris Graduate School for Mathematical Sciences (PGSM). My studies have been generously supported by the Fondation Sciences Mathématiques de Paris. I completed my first year of the Master’s program in Mathematics and my undergraduate degree in Mathematics and Computer Science at
Chennai Mathematical Institute (CMI). My research primarily focuses on number theory, with particular interests in analytic number theory and arithmetic statistics. My CV.
email: hrishabh.mishra[@]etu.u-paris.fr, hrishabh[@]cmi.ac.in
Belvédère de Sugiton, Marseille, France.
Preprints
Integral Hasse principle for Markoff type cubic surfaces (with an appendix by Victor Y. Wang)
(arXiv:2408.06846).On Malle's conjecture for the product of symmetric and nilpotent groups (with Anwesh Ray)
(arXiv:2402.01189).Upper bounds for the number of number fields with prescribed Galois group (with Anwesh Ray)
(arXiv:2310.00601).Counting number fields whose Galois group is a wreath product of symmetric groups (with Anwesh Ray)
(arXiv:2306.15411).-
On the number of subrings of \(\mathbb{Z}^n\) of prime power index (with Anwesh Ray)
(arXiv:2211.16595).
Talks and Presentations
Most odd-degree binary forms fail to primitively represent a square - summer 2024, Browning group, ISTA.
Frobenius distributions of Drinfeld modules - fall 2023, Chennai Mathematical Institute.
Malle's Conjecture for wreath products - fall 2023, Number theory seminar at Chennai Mathematical Institute.
Miscellaneous
Titchmarsh divisor problem in short intervals [pdf]. This proves an approximate formula for the sum \(\sum_{n \leq x} \Lambda(n)\tau(n-1)\) involving zeros of Dirichlet \(L\)-functions. Using the approximate formula we obtain asymptotics for \(\sum_{x < n \leq x+y}\Lambda(n)\tau(n-1)\) where \(x^{\theta} < y < x\) for suitable \(0 < \theta < 1\).
Integral points on Markoff type cubic surfaces [poster]. A poster created to explain the main result of the paper Integral Hasse Principle for Markoff type Cubic Surfaces to a general audience.
Frobenius distributions of Drinfeld modules of any rank [pdf]. A short write-up based on my talk for a course assessment on Drinfeld modules. In this write-up, I discuss the main result from the paper Frobenius Distributions of Drinfeld Modules of Any Rank by C. David.