69 citations · 615 across the 125 of their papers we have counts for
14 papers · 1 filter
Height zeta functions of equivariant compactifications of unipotent groups
Joseph Shalika, Yuri Tschinkel
We prove Manin's conjecture for bi-equivariant compactifications of unipotent groups.
Variation of Neron-Severi ranks of reductions of K3 surfaces
Edgar Costa, Yuri Tschinkel
We study the behavior of geometric Picard ranks of K3 surfaces over the rationals under reduction modulo primes. We compute these ranks for reductions of smooth quartic surfaces mo…
Multiple Mixing for adele groups and rational points
Alexander Gorodnik, Ramin Takloo-Bighash, Yuri Tschinkel
We prove an asymptotic formula for the number of rational points of bounded height on projective equivariant compactifications of $H\G$, where is a connected simple algebraic g…
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…
Integral points of bounded height on compactifications of semi-simple groups
Ramin Takloo-Bighash, Yuri Tschinkel
We study the asymptotic distribution of integral points of bounded height on partial bi-equivariant compactifications of semi-simple groups of adjoint type.
Integral points of bounded height on toric varieties
Antoine Chambert-Loir, Yuri Tschinkel
We establish asymptotic formulas for the number of integral points of bounded height on toric varieties.
Integral points of bounded height on partial equivariant compactifications of vector groups
Antoine Chambert-Loir, Yuri Tschinkel
We establish asymptotic formulas for the number of integral points of bounded height on partial equivariant compactifications of vector groups.
Igusa integrals and volume asymptotics in analytic and adelic geometry
Antoine Chambert-Loir, Yuri Tschinkel
We establish asymptotic formulae for volumes of height balls in analytic varieties over local fields and in adelic points of algebraic varieties over number fields, relating the Me…
Universal torsors over Del Pezzo surfaces and rational points
Ulrich Derenthal, Yuri Tschinkel
We discuss Manin's conjecture concerning the distribution of rational points of bounded height on Del Pezzo surfaces, and its refinement by Peyre, and explain applications of unive…
Rational points on compactifications of semi-simple algebraic groups
Joseph A. Shalika, Ramin Takloo-Bighash, Yuri Tschinkel
We prove Manin's conjecture concerning the distribution of rational points of bounded height, and its refinement by Peyre, for wonderful compactifications of semi-simple algebraic…
Height zeta functions of equivariant compactifications of the Heisenberg group
Joseph Shalika, Yuri Tschinkel
We study analytic properties of height zeta functions of equivariant compactifications of the Heisenberg group.
On the distribution of points of bounded height on equivariant compactifications of vector groups
Antoine Chambert-Loir, Yuri Tschinkel
We prove asymptotic formulas for the number of rational points of bounded height on smooth equivariant compactifications of the affine space. (Nous établissons un développement asy…
Points of bounded height on equivariant compactifications of vector groups, II
Antoine Chambert-Loir, Yuri Tschinkel
We prove asymptotic formulas for the number of rational points of bounded height on certain blow-ups of the projective space.
Points of bounded height on equivariant compactifications of vector groups, I
Antoine Chambert-Loir, Yuri Tschinkel
We prove asymptotic formulas for the number of rational points of bounded height on certain equivariant compactifications of the affine plane.