29 citations · 127 across the 38 of their papers we have counts for
9 papers · 1 filter
Campana points on wonderful compactifications
Dylon Chow, Daniel Loughran, Ramin Takloo-Bighash +1
We prove a variant of Manin's conjecture for Campana points on wonderful compactifications of semi-simple algebraic groups of adjoint type. We use this to provide evidence for a ne…
Campana points, Height zeta functions, and log Manin's conjecture
Sho Tanimoto
This is a report of the author's talk at RIMS workshop 2020 Problems and Prospects in Analytic Number Theory held online on Zoom. We discuss a recent formulation of log Manin's con…
Campana points of bounded height on vector group compactifications
Marta Pieropan, Arne Smeets, Sho Tanimoto +1
We initiate a systematic quantitative study of subsets of rational points that are integral with respect to a weighted boundary divisor on Fano orbifolds. We call the points in the…
On upper bounds of Manin type
Sho Tanimoto
We introduce a certain birational invariant of a polarized algebraic variety and use that to obtain upper bounds for the counting functions of rational points on algebraic varietie…
Zero-loci of Brauer group elements on semi-simple algebraic groups
Daniel Loughran, Ramin Takloo-Bighash, Sho Tanimoto
We consider the problem of counting the number of rational points of bounded height in the zero-loci of Brauer group elements on semi-simple algebraic groups over number fields. We…
Effective bounds for Brauer groups of Kummer surfaces over number fields
Victoria Cantoral-Farfán, Yunqing Tang, Sho Tanimoto +1
We study effective bounds for Brauer groups of Kummer surfaces associated to the Jacobians of curves of genus defined over number fields.
Distribution of rational points of bounded height on equivariant compactifications of I
Ramin Takloo-Bighash, Sho Tanimoto
We study the distribution of rational points of bounded height on a one-sided equivariant compactification of using automorphic representation theory of $\mathrm{P…
The distribution of -integral points on -orbit closures of binary forms
Sho Tanimoto, James Tanis
We study the distribution of -integral points on -orbit closures of binary forms and prove an asymptotic formula for the number of -integral points of bounded…
Height zeta functions of equivariant compactifications of semi-direct products of algebraic groups
Sho Tanimoto, Yuri Tschinkel
We apply the theory of height zeta functions to study the asymptotic distribution of rational points of bounded height on projective equivariant compactifications of semi-direct pr…