Publications

• Thin bases of order h, Journal of Number Theory 98 (2003), 34-46 (abstract)
• On cusp forms associated with binary theta series, Archiv der Mathematik 82 (2004), 140-146 (abstract)
• Binary quadratic forms with large discriminants and sums of two squareful integers, Crelle's Journal 569 (2004), 213-234 (abstract)
• Uniform bounds for Fourier coefficients of theta series with arithmetic applications, Acta Arithmetica 114, (2004), 1-21 (abstract)
• Shifted convolution sums and subconvexity bounds for automorphic L-functions, IMRN 2004, no. 73, 3905-3926 (abstract)
• Nonvanishing of class group L-functions at the central point, Annales de l'Institut Fourier 54 (2004), 831-847 (abstract)
• Binary quadratic forms with large discriminants and sums of two squareful integers II, J. London Math. Soc. 71 (2005), 69-84 (abstract)
• A three squares theorem with almost primes (with J. Brüdern), Bulletin of the London Mathematical Society 37 (2005), 507-513 (abstract)
• Rankin-Selberg L-functions on the critical line, manuscripta mathematica 117 (2005), 111-133 (abstract)
• On the number of integers represented by systems of Abelian norm forms (with J.-C. Schlage-Puchta), Acta Arith. 123 (2006), 183-199 (abstract)
• Estimates for representation numbers of quadratic forms (with A. Granville), Duke Math. Journal 135 (2006), 261-302 (abstract)
• A Burgess-like subconvex bound for twisted L-functions (with appendix 2 by Z.Mao) (with G. Harcos and P. Michel), Forum Math. 19 (2007), 61-106 (abstract)
• Bounds for modular L-functions in the level aspect (with G.Harcos and P.Michel), Ann. Sci. Ecole Norm. Sup. 40 (2007), 697-740 (abstract)
• Prime paucity for sums of two squares (with J. Brüdern), Bull. Lond. Math. Soc. 40 (2008), 457-462 (abstract)
• Sums of Hecke eigenvalues over values of quadratic polynomials, IMRN 2008 art. ID rnn059, 29pp. (abstract, arxiv)
• Hybrid bounds for twisted L-functions (with G. Harcos), Crelle's Journal 621 (2008), 53-79 (abstract); Addendum Crelle's Journal 694 (2014), 241-244
• Spectral decomposition of shifted convolution sums (with G. Harcos), Duke Math. J. 144 (2008), 321-339 (abstract, arxiv)
• The average value of divisor sums in arithmetic progressions, Quart. J. Math. 59 (2008), 275-286 (abstract)
• Ternary quadratic forms and sums of three squares with multiplicative restrcitions, in: The Anatomy of Integers, J.-M. de Koninck, A. Granville, F. Luca (eds.), CRM proceedings and lecture notes 46 (2008), 1-17
• On the central value of symmetric square L-functions, Math. Z. 260 (2008), 755-777 (abstract)
• A quadric with arithmetic paucity (with J. Brüdern), Quart. J. Math. 60 (2009), 283-290 (abstract)
• Sums of smooth squares (with J. Brüdern and R. Dietmann), Compositio Math. 145 (2009), 1401-1441 (abstract)
• Bounding sup-norms of cusp forms of large level (with R. Holowinsky), Invent. Math. 179 (2010), 645-681 (abstract, arxiv)
• The number of integer points on Vinogradov's quadric (with J. Brüdern), Monatsh. Math. 160 (2010), 243-256 (abstract)
• Iterates of Vinogradov's quadric and prime paucity (with J. Brüdern), Michigan Math. J. 59 (2010), 231-240
• Twisted L-functions over number fields and Hilbert's eleventh problem (with G. Harcos), GAFA 20 (2010), 1-52 (arxiv)
• Subconvexity for a double Dirichlet series, Compositio Math. 147 (2011), 355-374 (arxiv)
• On the Ramanujan conjecture over number fields (with F. Brumley), Annals of Math. 174 (2011), 581-605 (arxiv)
• Sup-norms of eigenfunctions on arithmetic ellipsoids (with P. Michel), IMRN 2011 no.21 (2011), 4934-4966
• The density of points on a certain cubic threefold (with J. Brüdern), in: Contributions in analytic and algebraic number theory, V. Blomer, P. Mihăilescu (eds.), Springer Proceedings in Mathematics 9 (2012), 1-15
• Friable values of binary forms (with A. Balog, C. Dartyge, G. Tenenbaum), Commentarii Math. Helv. 87 (2012), 639-667 (abstract)
• A hybrid asymptotic formula for the second moment of Rankin-Selberg L-functions (with G. Harcos), Proc. Lond. Math. Soc. 105 (2012), 473-505 (arxiv)
• Subconvexity for twisted L-functions on GL(3), Amer. J. Math. 134 (2012), 1385-1421
• Period integrals and Rankin-Selberg L-functions on GL(n), Geom. Funct. Anal. 22 (2012), 608-620 (arxiv)
• Non-vanishing of L-functions, the Ramanujan conjecture, and families of Hecke characters (with F. Brumley), Canad. J. Math. 65 (2013), 22-51 (arxiv)
• On the 4-norm of an automorphic form, J. Eur. Math. Soc. 15 (2013), 1825-1852 (arxiv)
• Hybrid bounds for automorphic forms on ellipsoids over number fields (with P. Michel), J. Inst. Math. Jussieu 12 (2013), 727-758 (arxiv)
• Distribution of mass of holomorphic cusp forms (with R. Khan and M. Young), Duke Math. J. 162 (2013), 2609-2644 (arxiv)
• Applications of the Kuznetsov formula on GL(3), Invent. Math. 194 (2013), 673-729 (arxiv)
• Twins of powerful numbers (with A. Schöbel), Funct. et Approx. 49 (2013), 349-356
• L-functions with n-th order twists (with L. Goldmakher and B. Louvel), IMRN 2014 (vol. 7), 1925-1955 (arxiv)
• On a certain senary cubic form (with J. Brüdern and P. Salberger), Proc. London Math. Soc. 108 (2014), 911-964 (arxiv)
• A Sato-Tate law for GL(3) (with J. Buttcane and N. Raulf), Comm. Math. Helv. 89 (2014), 895-919 (abstract)
• Bounding hyperbolic and spherical coefficients of Maass forms (with F. Brumley, A. Kontorovich, N. Templier), J. Théorie Nombres (Bordeaux) 26 (2014), 559-578
• Kloosterman sums in residue classes (with D. Milićević), J. Eur. Math. Soc. 17 (2015), 51-69 (arxiv)
• The second moment of twisted modular L-functions (with D. Milićević), Geom. Funct. Anal. 25 (2015), 453-516
• The sup-norm problem for PGL(4) (with P. Maga), IMRN 2015 (vol. 14), 5311-5332 (arxiv)
• Number fields without universal n-ary quadratic forms (with V. Kala), Math. Proc. Cambr. Phil. 159 (2015), 239-252 (arxiv)
• p-adic analytic twists and strong subconvexity (with D. Milićević), Ann. Sci. Ec. Norm. Sup. 48 (2015), 561-605
• On the size of Ikeda lifts, manuscr. math. 148 (2015), 341-349
• Bounds for eigenforms on arithmetic hyperbolic 3-manifolds (with G. Harcos and D. Milićević), Duke Math. J. 165 (2016), 625-659 (arxiv)
• Subconvexity for sup-norms of cusp forms on PGL(n) (with P. Maga), Selecta Math. 22 (2016), 1269-1287 (arxiv)
• The sup-norm problem on the Siegel modular space of rank two (with A. Pohl), Amer. J. Math. 136 (2016), 999-1027 (arxiv)
• A note on the negative Pell equation, in: From Arithmetic to Zeta Functions: Number Theory in Memory of Wolfgang Schwarz, J. Sander, J. Steuding, R. Steuding (eds.), Springer-Verlag 2016, pp.31-40
• On moments of twisted L-functions (with E. Fouvry, E. Kowalski, P. Michel and D. Milićević), Amer. J. Math. 137 (2017), 707-768 (arxiv)
• Applications of smooth bilinear sums of Kloosterman sums (with E. Fouvry, E. Kowalski, P. Michel and D. Milićević), Proceedings of the Steklov Institute of Mathematics (memorial volume for I. M. Vinogradov) 296 (2017), 24-35 (arxiv)
• On triple correlations of divisor functions, Bull. Lond. Math. Soc. 49 (2017), 10-22 (arxiv)
• Applications of the Kuznetsov formula on GL(3) II: the level aspect (with J. Buttcane and P. Maga), Math. Ann. 369 (2017), 723-759 (arxiv)
• Small gaps in the spectrum of the rectangular billard (with J. Bourgain, M. Radziwiłł and Z. Rudnick), Ann. Sci. Ecole Norm. Sup. 50 (2017), 1283-1300 (arxiv)
• Rational points on the inner product cone via the hyperbola method (with J. Brüdern), Mathematika 63 (2017) Special issue in honour of Klaus Roth, 780-796 (arxiv)
• The Manin-Peyre conjecture for a certain biprojective cubic threefold (with J. Brüdern and P. Salberger), Math. Ann. 370 (2018), 491-553 (arxiv)
• Counting in hyperbolic spikes: the diophantine analysis of multihomogeneous diagonal equations (with J. Brüdern), J. Reine Angew. Math. 737 (2018), 255-300 (arxiv)
• On the rank of universal quadratic forms over real quadratic fields (with V. Kala), Doc. Math. 23 (2018), 15-34 (arxiv)
• Higher order divisor problems, Math. Z. 290 (2018), 937-952 (arxiv)
• On the global sup-norm of GL(3) cusp forms (with G. Harcos and P. Maga), Israel J. Math. 229 (2019), 357-379 (arxiv)
• Uniform subconvexity and symmetry breaking reciprocity (with R. Khan), J. Funct. Anal. 276 (2019), 2315-2358 (arxiv)
• Twisted moments of L-functions and spectral reciprocity (with R. Khan), Duke Math. J. 168 (2019), 1109-1177 (arxiv)
• Spectral summation formula for GSp(4) and moments of spinor L-functions, J. Eur. Math. Soc. 21 (2019), 1751-1774 (arxiv)
• A spectral reciprocity formula and non-vanishing for L-functios on GL(4) x GL(2) (with X. Li and S. Miller), J. Number Theory Prime 205 (2019), 1-43 (arxiv)
• Global decomposition of GL(3) Kloosterman sums and the spectral large sieve (with J. Buttcane), J. Reine Angew. Math. 757 (2019), 51-88 (arxiv)
• Subconvexity for L-functions of non-spherical cusp forms on GL(3) (with J. Buttcane), Acta Arith. 192 (2020), 31-62 (arxiv)
• The sup-norm problem for GL(2) over number fields (with G. Harcos, P. Maga, D. Milićević), J. Eur. Math. Soc. 22 (2020), 1-53 (arxiv)
• Epstein zeta function, subconvexity, and the purity conjecture, J. Inst. Math. Jussieu 19 (2020), 581-596 (arxiv)
• Motohashi's fourth moment identity with non-archimedean test functions and applications (with P. Humphries, R. Khan, M. Milinovich), Compositio Math. 156 (2020), 1004-1038 (arxiv)
• Analytic properties of cusp forms on GL(n) (with G. Harcos and P. Maga), J. Anal. Math. 140 (2020), 483-510 (arxiv)
• On the subconvexity problem for L-functions on GL(3) (with J. Buttcane), Ann. Sci. Ecole Norm. Sup. 53 (2020), 1441-1500 (arxiv)
• Uniform Titchmarsh divisor problems (with E. Assing, J. Li), Adv. Math. 393 (2021), Paper No. 108076, 50pp. (arxiv)
• A symplectic restriction problem (with A. Corbett), Math. Ann. 382 (2022), 1323-1424 (arxiv)
• Beyond the spherical sup-norm problem (with G. Harcos, P. Maga, D. Milićević), J. Math. Pures Appl. 168 (2022), 1-64 (arxiv)
• The second moment theory of families of L-functions (with E. Fouvry, E. Kowalski, P. Michel, D. Milićević, W. Sawin), Memoirs AMS 282 no.1394 (2023), 150pp. (arxiv)
• Density theorems for GL(n), Invent. Math. 232 (2023), 683-711 (arxiv)
• The Weyl bound for triple product L-functions (with S. Jana and P. Nelson), Duke Math. J. 172 (2023), 1173-1234 (arxiv)
• Small gaps in the spectrum of tori: asymptotic formulae (with M. Radziwiłł), Comm. Math. Phys. 403 (2023), 155-180 (arxiv)
• Additive problems with almost prime squares (with L. Grimmelt, J. Li and S. Rydin Myerson), GAFA 33 (2023), 1173-1242 (arxiv)
• Correlations of values of random diagonal forms (with J. Li), IMRN 2023 (2023), 20296-20336 (arxiv)
• The unipotent mixing conjecture (with P. Michel), J. Anal. Math. (special volume for Peter Sarnak) 151 (2023), 25-57 (arxiv)
• The Manin-Peyre conjecture for smooth spherical Fano varieties of semisimple rank one (with J. Brüdern, U. Derenthal, G. Gagliardi), Forum Math. Sigma 12 (2024), e11, 93pp. (arxiv)
• Triple correlation and long gaps in the spectrum of flat tori (with C. Aistleitner, M. Radziwiłł), J. Eur. Math. Soc. 26 (2024), 41-74 (arxiv)
• Simultaneous equidistribution of toric periods and fractional moments of L-functions (with F. Brumley), J. Eur. Math. Soc. 26 (2024), 2745-2796 (arxiv)
• The density conjecture for principal congruence subgroups (with E. Assing), Duke Math. J. 173 (2024), 1359-1426 (arxiv)
• Hyperbolic lattice point counting in unbounded rank (with C. Lutsko), J. Reine Angew. Math. 812 (2024), 257-274 (arxiv)
• The Manin-Peyre conjecture for smooth spherical Fano threefolds (with J. Brüdern, U. Derenthal, G. Gagliardi), Selecta Math. 30 (2024), Paper No. 69, 61pp. (arxiv)
• Bounds for Kloosterman sums on GL(n) (with S. H. Man), Math. Ann. 390 (2024), 1171-1200 (arxiv)
• Moments of symmetric square L-functions on GL(3) (with F. Comtat), Proc. Lond. Math. Soc. 130 (2025), Paper e70033, 44pp. (arxiv)
• Local integral transforms and global spectral decomposition (with S. Jana, P. Nelson), GAFA 35 (2025), 1051-1107 (arxiv)
• Triple sums of Kloosterman sums and the discrepancy of modular inverses (with M. Risager und I. Shparlinski), J. Lond. Math. Soc. 112 (2025), e70291, 30pp. (arxiv)
• A GL(3) converse theorem via a "beyond endoscopy" approach (with W. H. Leung), Adv. Math. 485 (2026), Art. 110716, 99pp. (arxiv)
• The mixing conjecture under GRH (with F. Brumley, I. Khayutin), Ann. Sci. Ecole Norm. Sup. 59 (2026), 437-500 (arxiv)
• Analytic properties of representation zeta functions for groups of type A_2 (with C. Voll), Math. Ann. 295, 72 (arxiv)
• Local Analysis of the Kuznetsov formula and the density conjecture (with E. Assing, P. Nelson), J. Math. Pures. Appl. 214 (2026), 103954, 43pp. (arxiv)
• The cost of cyclic permutations and remainder sums in the Euclidean Algorithm (with K.-U. Bux), LIPIcs 381 Analysis of Algorithms 2026, Art. No. 14, 17pp. (arxiv)
• Zeros of L-functions in families near the critical line (with J. Thorner), to appear in Trans. Amer. Math. Soc., 20pp. (arxiv)

  Preprints (submitted)

  • Generation of Hecke fields by squares of cyclotomic twists of modular L-values (with A. Burungale, P. Michel, J.-H. Min), 30pp. (arxiv)
  • A higher rank shifted convolution problem with applications to L-functions (with J. Li), 30pp. (arxiv)
  • Pair correlation for modular inverses, 20pp.
  • Joint Linnik problems (with F. Brumley and M. Radziwiłł), 50pp. (arxiv)
  • Moments and joint non-vanishing of symplectic L-functions (with S. Das), 20pp. (arxiv)
  • Bilinear forms with Kloosterman sums via quadratic characters (with A. Pascadi), 30pp. (arxiv)

  Survey Articles

  • The theorem of Green-Tao Newsletter of the European Math. Soc. 67 (2008), 13-16
    German version: Mitteilungen DMV 15 (2007) 160-164
    Chinese version: Mathematical Advance in Translation 27 (2008), 203-207
  • L-functions, automorphic forms and arithmetic (with G. Harcos), in: Symmetries in Algebra and Number Theory, R. Meyer, I. Kersten (eds.), Universitätsverlag Göttingen 2009, 11-26
  • The role of the Ramanujan conjecture in analytic number theory (with F. Brumley), Bulletin AMS 50 (2013), 267-320
  • The relative trace formula in analytic number theory, in: Relative trace formulas, W. Müller, S. W. Shin, N. Templier (eds.) Simons Symp., Springer-Verlag 2021, 51-73 (arxiv)
  • Was ist eine Modulform oder Wozu brauchen wir gekrümmte Räume? (in German), to appear in Mitt. DMV
  • Automorphic density theorems and applications to appear in ICM proceedings 2026

  Books edited

  • Contributions in analytic and algebraic number theory. Festschrift for S. J. Patterson (with P. Mihăilescu), Springer Proceedings in Mathematics 9, Springer 2012, 290 + xviii pages

  Some (mostly typographical) corrections can be found here. I provide copies of these papers on request. The arxiv versions may differ from the published versions.
  
  

  Submission statistics
  Longest waiting time for acceptance: 46 months, 41 months, 33 months, 27 months, 25 months
  Longest waiting time for rejection: 38 months (based on a "quick opinion")
  Shortest waiting time for acceptance: 2 weeks (fully refereed)
  Average number of subissions per paper: ≈1.3 times
  
  

  Last Update: March 2026