Publications

Papers in Journals

• 1. D. Kelmer, A. Kontorovich, C. Lutsko Norm bounds on  Eisenstein series. Int. J. Number Theory 20 (8), 2083-2098 (2024),.

  2. D. Kelmer, S. Yu Second moment of the light-cone Siegel transform and applications. Adv. Math. 432 (2023), Paper No. 109270, 70 pp.

  3.  D. Kelmer, A. Kontorovich, C. Lutsko Sarnak’s spectral gap question.J. Anal. Math. 151 (2023), no. 1, 171–179.

  4.  D. Kelmer, S. Yu Fourier expansion of light-cone Eisenstein series. J. Lond. Math. Soc. (2) 108 (2023), no. 6, 2175–2247.

  5. A. Ghosh, D. Kelmer and  S. Yu Effective density for inhomogeneous quadratic forms II: fixed forms and generic shifts. Int. Math. Res. Not. (2023), no. 22, 19507–19545.

  6.  A. Ghosh, D. Kelmer and  S. Yu Effective density for inhomogeneous quadratic forms I: generic forms and fixed shifts. Int. Math. Res. Not. (2022), no. 6, 4682–4719.

  7.  D. Kelmer and S. Yu Values of random polynomials in shrinking targets.  Trans. Amer. Math. Soc. 373 (2020), no. 12, 8677–8695

  8.  D. Kelmer and H. Oh Exponential mixing and shrinking targets for geodesic flow on geometrically finite hyperbolic manifolds.  J. Mod. Dyn. 17 (2021), 401–434

  9. D. Kelmer and S. Yu Shrinking targets problems for flows on homogeneous spaces. Trans. Amer. Math. Soc. 372 (2019), no. 9, 6283–6314

  10. D. Kelmer and S. Yu The second moment of the Siegel transform in the space of symplectic lattices. Int. Math. Res. Not. (2019) 

  11. D. Kelmer and A. Kontorovich Exponents for the Equidistribution of Shears and Applications.  J. Number Theory 208 (2020), 1–46.

  12. D. Kelmer Shrinking targets for discrete time flows on hyperbolic manifolds. Geom. Funct. Anal. 27 (no. 5), 1257-1287,(2017)

  13. D. Kelmer Approximation of points in the plane by generic lattice orbits. J. Mod. Dyn. 11, 143-153, (2017).

  14. A. Ghosh and D. Kelmer A Quantitative Oppenheim Theorem for generic ternary quadratic forms.  J. Mod. Dyn. 12, 1-8, (2018).

  15. D. Kelmer On the mean square of the remainder for the Euclidean lattice point counting problem . Israel J. Math. 221 (no. 2), 637-659, (2017).

  16. A. Ghosh and D. Kelmer Shrinking targets for semisimple groups. Bull. Lond. Math. Soc. 49 (no. 2), 235-245, (2017).

  17. D. Kelmer Lattice points in a circle for generic unimodular shears. Int. J. Number Theory 13 (no. 2), 291-300, (2017).

  18. D. Kelmer and A. Kontorovich Effective equidistribution of shears and applications. Math. Ann. 370 (no. 1-2), 381-421 (2017).

  19. D. Kelmer On distribution of poles of Eisenstein series and the length spectrum of hyperbolic manifolds. Int. Math. Res. Not. Vol. 2015, 12319-12344 (2015)

  20. D. Kelmer and A. Kontorovich, On the Pair Correlation Density for Hyperbolic Angles. Duke Math. J. 164, 473-509 (2015)

  21. D. Kelmer, Hybrid trace formula for a non-uniform irreducible lattice in PSL(2,R)n. J. Number Theory (133), no. 7, 2277-2306. (2013).

  22. D. Kelmer, Quadratic irrationals and linking numbers of modular knots. J. Mod. Dyn. (6), no. 4, 539-561 (2012).

  23. D. Kelmer, A refinement of strong multiplicity one for spectra of hyperbolic manifolds. Tran. Amer. Soc. 366, 5925-5961 (2014).

  24. D. Kelmer and A. Mohammadi, Logarithm laws for one parameter unipotent flows. Geom. Funct. Anal. 22, no. 3, 756-784 (2012).

  25. D. Kelmer and L. Silberman, A uniform spectral gap for congruence covers of a hyperbolic manifold. Amer. J. Math. 135, no. 4, 1067-1085 (2013).

  26. D. Kelmer, A uniform strong spectral gap for congruence covers of a compact quotient of PSL(2,R)^d. Int. Math. Res. Not. (2011) 1135-1164 (2011).

  27. D. Kelmer, Distribution of holonomy about closed geodesics in a product of hyperbolic planes. Amer. J. Math. (134), no. 6, 1613-1653 (2012)

  28. D. Kelmer and Peter Sarnak, Strong Spectral Gaps for Compact Quotients of Products of PSL(2,R). J. Eur. Math. Soc. 11 (2), 283-313 (2009).

  29. D. Kelmer, On matrix elements for the quantized cat map modulo prime powers. Ann. Henri Poincaré 9 (8), 1479-1501 (2008).

  30. D. Kelmer, Distribution of twisted Kloosterman sums modulo prime powers. Int. J. Num. Theory 6 (2), 271-280 (2010).

  31. D. Kelmer, Scarring for Quantum Maps with Simple Spectrum. Compos. Math. 147, 1608-1612 (2011).

  32. D. Kelmer, Quantum Ergodicity for products of hyperbolic planes. J. Mod. Dyn. 2 (2), 287-313 (2008).

  33. L. Bary-Soroker and D. Kelmer, On PAC extensions and scaled Trace forms. Israel J. Math. (175), 113-125 (2010).

  34. D. Kelmer, Scarring on invariant manifolds for perturbed quantized hyperbolic toral automorphisms. Comm. Math. Phys. 276 (2), 381-395 (2007).

  35. D. Kelmer, Arithmetic Quantum Unique Ergodicity for Symplectic Linear Maps of the Multidimensional Torus. Ann. of Math. 171 (2), 815-879 (2010).

  36. D. Kelmer, On the quantum variance of matrix elements for the cat map on the 4-dimensional torus. Int. Math. Res. Not. 36, 2223-2236 (2005).

Preprints

• 1. D. Kelmer, A. Kontorovich, C. Lutsko Sign changes along geodesics of modular forms Preprint arXiv:2409.17248.

  2. D. Kelmer, Effective density of values of indefinite ternary inhomogeneous quadratic forms Preprint arXiv:2408.03153.

  3. D. Kelmer, Counting rational points on the sphere with bounded denominator Preprint arXiv:2404.02114.