Research


Papers

25. Peter Humphries and Jesse Thorner, "New Variants of Arithmetic Quantum Ergodicity", submitted for publication (2024), 28 pages. (arXiv)

24. Ankit Bisain, Peter Humphries, Andrei Mandelshtam, Noah Walsh, and Xun Wang, "Subconvexity Implies Effective Quantum Unique Ergodicity for Hecke–Maaß Cusp Forms on SL₂(ℤ)\SL₂(ℝ)", submitted for publication (2024), 24 pages. (arXiv)

23. Peter Humphries and Asbjørn Christian Nordentoft, "Sparse Equidistribution of Geometric Invariants  of Real Quadratic Fields", submitted for publication (2022), 57 pages. (arXiv)

22. Peter Humphries and Rizwanur Khan, "Lᵖ-Norm Bounds for Automorphic Forms via Spectral Reciprocity", submitted for publication (2022), 60 pages. (arXiv)

21. Peter Humphries, "Archimedean Newform Theory for GLn", to appear in Journal of the Institute of Mathematics of Jussieu (2024), 76 pages. (journal | arXiv)

20. Peter Humphries, "The Newform K-Type and p-adic Spherical Harmonics", to appear in Israel Journal of Mathematics (2022), 38 pages. (journal | arXiv)

19. Peter Humphries and Rizwanur Khan, "The Twelfth Moment of Hecke L-Functions in the Weight Aspect", Mathematische Annalen 389:4 (2024), 3935–3974. (journal | arXiv | MathSciNet)

18. Peter Humphries and Jesse Thorner, "Zeros of Rankin–Selberg L-Functions in Families", Compositio Mathematica 160:5 (2024), 1041–1072. (journal | arXiv | MathSciNet)

17. Peter Humphries and Yeongseong Jo, "Test Vectors for Archimedean Period Integrals", Publicacions Matemàtiques 68:1 (2024), 139–185. (journal | arXiv | MathSciNet)

16. Peter Humphries and Maksym Radziwiłł, "Optimal Small Scale Equidistribution of Lattice Points on the Sphere, Heegner Points, and Closed Geodesics", Communications on Pure and Applied Mathematics 75:9 (2022), 1936–1996. (journal | arXiv | MathSciNet)

15. Peter Humphries, "Distributing Points on the Torus via Modular Inverses", The Quarterly Journal of Mathematics 73:1 (2022), 1–16. (journal | arXiv | MathSciNet)

14. Peter Humphries and Jesse Thorner, "Towards a GLn Variant of the Hoheisel Phenomenon", Transactions of the American Mathematical Society 375:3 (2022), 1801–1824. (journal | arXiv | MathSciNet)

13. Peter Humphries, "Test Vectors for Non-Archimedean Godement–Jacquet Zeta Integrals", Bulletin of the London Mathematical Society 53:1 (2021), 92–99. (journal | arXiv | MathSciNet)

12. Valentin Blomer, Peter Humphries, Rizwanur Khan, and Micah B. Milinovich, "Motohashi's Fourth Moment Identity for Dirichlet L-Functions for Non-Archimedean Test Functions and Applications", Compositio Mathematica 156:5 (2020), 1004–1038. (journal | arXiv | MathSciNet)

11. Peter Humphries and Rizwanur Khan, "On the Random Wave Conjecture for Dihedral Maaß Forms", Geometric and Functional Analysis 30:1 (2020), 34–125. (journal | arXiv | MathSciNet)

10. Peter Humphries, "Spectral Multiplicity for Maaß Newforms of Non-Squarefree Level", International Mathematics Research Notices 2019:18 (2019), 5703–5743. (journal | arXiv | MathSciNet)

9. Peter Humphries, Snehal M. Shekatkar, and Tian An Wong, "Biases in Prime Factorizations and Liouville Functions for Arithmetic Progressions", Journal de Théorie des Nombres de Bordeaux 31:1 (2019), 1–25. (journal | arXiv | MathSciNet)

8. Peter Humphries, "Standard Zero-Free Regions for Rankin–Selberg L-Functions via Sieve Theory", with an appendix by Farrell Brumley, Mathematische Zeitschrift 292:3–4 (2019), 1105–1122. (journal | arXiv | MathSciNet)

7. Peter Humphries, "Density Theorems for Exceptional Eigenvalues for Congruence Subgroups", Algebra & Number Theory 12:7 (2018), 1581–1610. (journal | arXiv | MathSciNet)

6. Peter Humphries, "Equidistribution in Shrinking Sets and L⁴-Norm Bounds for Automorphic Forms", Mathematische Annalen 371:3–4 (2018), 1497–1543. (journal | arXiv | MathSciNet)

5. Peter Humphries, "Effective Lower Bounds for L(1,χ) via Eisenstein Series", Pacific Journal of Mathematics 288:2 (2017), 355–375. (journal | arXiv | MathSciNet)

4. Kiril Datchev, Jesse Gell-Redman, Andrew Hassell, and Peter Humphries, "Approximation and Equidistribution of Phase Shifts: Spherical Symmetry", Communications in Mathematical Physics 326:1 (2014), 209–236. (journal | arXiv | MathSciNet)

3. Peter Humphries, "On the Mertens Conjecture for Elliptic Curves over Finite Fields", Bulletin of the Australian Mathematical Society 89:01 (2014), 19–32. (journal | arXiv | MathSciNet)

2. Peter Humphries, "On the Mertens Conjecture for Function Fields", International Journal of Number Theory 10:2 (2014), 341–361. (journal | arXiv | MathSciNet)

1. Peter Humphries, "The Distribution of Weighted Sums of the Liouville Function and Pólya's Conjecture", Journal of Number Theory 133:2 (2013), 545–582. (journal | arXiv | MathSciNet)


Errata