{"id":377,"date":"2020-09-07T16:15:52","date_gmt":"2020-09-07T16:15:52","guid":{"rendered":"https:\/\/dchatzakos.math.upatras.gr\/?page_id=377"},"modified":"2026-04-02T17:01:27","modified_gmt":"2026-04-02T15:01:27","slug":"page_id377","status":"publish","type":"page","link":"https:\/\/dchatzakos.math.upatras.gr\/?page_id=377","title":{"rendered":"Research"},"content":{"rendered":"\r\n

Research interests<\/strong><\/p>\r\n\r\n\r\n\r\n

Automorphic forms, Spectral theory, Analytic number theory<\/p>\r\n

My current research interests lie on problems related to L-functions of Maass forms<\/a> and Quantum Unique Ergodicity<\/a>. I am also interested on\u00a0 counting problems in the spectral theory of automorphic forms, such as Prime Geodesic theorems and Lattice counting problems.<\/p>\r\n

I finished my PhD\u00a0in Pure Mathematics at UCL, UK<\/a>\u00a0under the supervision of Yiannis Petridis<\/a>. In my thesis I worked on two different hyperbolic lattice counting problems. The classical hyperbolic lattice point problem is the hyperbolic analogue of the Gauss\u2019 circle problem<\/a>. I studied various modifications of it, as well as arithmetic applications of them.<\/p>\r\n

You can find my thesis here<\/a>.<\/p>\r\n\r\n\r\n\r\n

Papers<\/strong><\/p>\r\n

1. <\/strong>The hyperbolic circle problem over Heegner points. (with G. Cherubini<\/a>, S. Lester<\/a> and M. Risager<\/a>, submitted for publication, arXiv<\/a>)<\/p>\r\n

2. <\/strong>Mean Values and Quantum Variance for Degenerate Eisenstein Series of Higher Rank. (with C. Darreye and I. Kaneko<\/a>), The Quarterly Journal of Mathematics (to appear), (arXiv<\/a>)<\/p>\r\n

3. <\/strong>The Prime Geodesic Theorem in Arithmetic Progressions. (with G. Harcos<\/a> and I. Kaneko<\/a>), Int. Math. Res. Not. IMRN (2024), no.20, 13180–13190. (arXiv<\/a>)\u00a0<\/p>\r\n

4. <\/strong>On the distribution of lattice points on hyperbolic circles. (with P. Kurlberg<\/a>, S. Lester<\/a> and I. Wigman<\/a>), Algebra & Number Theory 15 (2021), no. 9, 2357–2380. (arXiv<\/a>)<\/p>\r\n

5.<\/strong> Quantum ergodicity for shrinking balls in arithmetic hyperbolic manifolds. (with R. Frot and N. Raulf<\/a>), (submitted for publication, arXiv<\/a>)<\/p>\r\n

6. <\/strong>Second Moment of the Prime Geodesic Theorem for PSL(2,Z[i]). (with G. Cherubini<\/a> and N. Laaksonen<\/a>), Math. Z. 300 (2022), no. 1, 791–806. (arXiv<\/a>)<\/p>\r\n

7. <\/strong>CM-points and lattice counting on arithmetic\u00a0compact Riemann surfaces. (with M. Alsina<\/a>),\u00a0 J. Number Theory 212 (2020), 339–353. (arXiv<\/a>)<\/p>\r\n

8.<\/strong> Prime Geodesic Theorem in the 3-dimensional Hyperbolic Space. (with O. Balkanova<\/a>,\u00a0G. Cherubini<\/a>, D. Frolenkov<\/a> and N. Laaksonen<\/a>), Trans. Amer. Math. Soc. 372 (2019), no. 8, 5355–5374. (arXiv<\/a>)<\/p>\r\n

9.<\/strong> Mean value and \u03a9-results for the hyperbolic lattice point problem in conjugacy classes. Rev. Mat. Iberoam. 35 (2019), no. 4, 1123–1152. (arXiv<\/a>)<\/p>\r\n

10.<\/strong> \u03a9-results for the hyperbolic lattice point problem. Proc. Amer. Math. Soc., vol. 145 (2017), no. 4, 1421–1437. (arXiv<\/a>)<\/p>\r\n\r\n\r\n\r\n

11.<\/strong> The hyperbolic lattice point problem in conjugacy classes. (with\u00a0Y. Petridis<\/a>), Forum Math. 28 (2016), no. 5, 981–1003. (arXiv<\/a>)<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n

Others<\/strong><\/p>\r\n\r\n\r\n\r\n

1.<\/strong>\u00a0The error term in term in the Prime Geodesic Theorem for hyperbolic 3-manifolds, (short review article in the Proceedings of the 16th Panhellenic Conference on Mathematical Analysis<\/a>)<\/p>\r\n","protected":false},"excerpt":{"rendered":"

Research interests Automorphic forms, Spectral theory, Analytic number theory My current research interests lie on problems related to L-functions of Maass forms and Quantum Unique Ergodicity. I am also interested on\u00a0 counting problems in the spectral theory of automorphic forms, such as Prime Geodesic theorems and Lattice counting problems. I finished my PhD\u00a0in Pure Mathematics […]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"_links":{"self":[{"href":"https:\/\/dchatzakos.math.upatras.gr\/index.php?rest_route=\/wp\/v2\/pages\/377"}],"collection":[{"href":"https:\/\/dchatzakos.math.upatras.gr\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/dchatzakos.math.upatras.gr\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/dchatzakos.math.upatras.gr\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/dchatzakos.math.upatras.gr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=377"}],"version-history":[{"count":29,"href":"https:\/\/dchatzakos.math.upatras.gr\/index.php?rest_route=\/wp\/v2\/pages\/377\/revisions"}],"predecessor-version":[{"id":624,"href":"https:\/\/dchatzakos.math.upatras.gr\/index.php?rest_route=\/wp\/v2\/pages\/377\/revisions\/624"}],"wp:attachment":[{"href":"https:\/\/dchatzakos.math.upatras.gr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=377"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}