PREPRINTS

• [6] Ping Xi, An elementary proof of the Selberg identity for Kloosterman sums, 3 pages, 2023, arXiv:2306.16929 [math.NT] (not for publication)

• [5] Ping Xi, A double character sum of Conrey-Iwaniec and Petrow-Young, 5 pages, 2023, arXiv:2302.14681 [math.NT]

• [4] Han Wu & Ping Xi, A uniform Weyl bound for L-functions of Hilbert modular forms, 36 pages, 2023, arXiv: 2302:14652 [math.NT]

• [3] Yong-Gao Chen & Ping Xi, A conjecture of Sárközy on quadratic residues, II, 12 pages, 2022, arXiv:2202.02780 [math.NT].

• [2] Daqing Wan & Ping Xi, Lang-Trotter conjecture for CM elliptic curves, 100 pages, 2021, arXiv:2109.14256 [math.NT].

• [1] Ping Xi, Equidistributions of Jacobi sums, 8 pages, 2018, preprint (not intending to submit).

PAPERS 

• [25] Ping Xi, Bilinear forms with trace functions over arbitrary sets, and applications to Sato-Tate, Sci. China Math. 66 (2023), 2819–2834.

• [24] Bryce Kerr, Igor Shparlinski, Xiaosheng Wu & Ping Xi, Bounds on bilinear forms with Kloosterman sums, J. London Math. Soc. 108 (2023), 578–621.

• [23] Ping Xi & Junren Zheng, Pythagoras equations and quadratic residues, to appear in Acta Math. Sinica, Chinese series (in Chinese).

• [22] Ping Xi, Moments and equidistributions of multiplicative analogues of Kloosterman sums, Acta Arith. 206 (2022), 245–275.

• [21] Jie Wu & Ping Xi, Arithmetic exponent pairs for algebraic trace functions and applications, with an appendix by Will Sawin,  Algebra Number Theory 15 (2021), 2123–2172.

• [20] Ping Xi, When Kloosterman sums meet Hecke eigenvalues, Invent. math. 220 (2020), 61-127.

• [19] Jianya Liu, Jie Wu & Ping Xi, Primes in arithmetic progressions with friable indices, Sci. China Math. 63 (2020), 23-38. 

• [18] Ping Xi & Yuan Yi, Kloosterman sums and a problem of D. H. Lehmer, Chinese Ann. Math. Ser. B. 41 (2020), 361-370.

• [17] Jie Wu & Ping Xi, Towards presentations of primes by polynomials, Proceedings of the Seventh International Congress of Chinese Mathematicians. Vol. II, 99-122, Adv. Lect. Math. (ALM), 44, Int. Press, Somerville, MA, 2019. 

• [16] Guangshi Lü & Ping Xi, On triple correlations of Fourier coefficients of cusp forms. II, Int. J. Number Theory 15 (2019), 713-722.

• [15] Ping Xi, Ternary divisor functions in arithmetic progressions to smooth moduli, Mathematika 64 (2018), 701-729.

• [14] Ping Xi, Counting fundamental solutions to the Pell equation with prescribed size, Compositio Math. 154 (2018), 2379-2402.

• [13] Ping Xi, A shifted convolution sum for $GL(3)\times GL(2)$, Forum Math. 30 (2018), 1013-1027.

• [12] Ping Xi, A quadratic analogue of Titchmarsh divisor problem, J. Number Theory 184 (2018), 192-205.

• [11] Guangshi Lü & Ping Xi, On triple correlations of Fourier coefficients of cusp forms,  J. Number Theory 183 (2018), 485-492.

• [10] Ping Xi, How strong can primes be, Acta Arith. 179 (2017), 363-373.

• [9] Ping Xi, Gaussian distributions of Kloosterman sums: vertical and horizental, Ramanujan J. 43 (2017), 493-511.

• [8] Ping Xi, Sign changes of Kloosterman sums with almost prime moduli. II, Int. Math. Res. Not. 4 (2018), 1200-1227. Corrigendum: Volume 2022, Issue 1, 556–574.

• [7] Jie Wu & Ping Xi, Quadratic polynomials at prime arguments, Math. Z. 285 (2017), 631-646. 

• [6] Ping Xi, Large sieve inequalities for algebraic trace functions, with an appendix by E. Fouvry, E. Kowalski and Ph. Michel, Int. Math. Res. Not. 16 (2017), 4840-4881. 

• [5] Ping Xi, Sign changes of Kloosterman sums with almost prime moduli, Monatsh. Math. 177 (2015), 141-163.

• [4] Ping Xi, Quadratic residues and non-residues for infinitely many Piatetski-Shaprio primes, Acta Math. Sinica, English Series 29 (2013), 515-522.

• [3] Ping Xi & Yuan Yi, A note on the moment of Kloosterman sums, Proc. Amer. Math. Soc. 141 (2013), 1233-1240. 

• [2] Ping Xi & Yuan Yi, Generalized D.H. Lehmer problem over short intervals, Glasgow Math. J. 53 (2011), 293-299. 

• [1] Ping Xi & Yuan Yi, On character sums over flat numbers, J. Number Theory 130 (2010), 1234-1240. 

UNPUBLISHED NOTES

• [3] Addendum to "Arithmetic exponent pairs of algebraic trace functions and applications",  arXiv:2104.14508

• [2] Construction of smooth functions, 2016 [required in many smoothing devices in analytic number theory]

• [1] On the greatest prime factors of $n^2+1$, 2016 [a reading note for the paper of Deshouillers-Iwaniec, prepared for "Seminar on Analytic Number Theory" in Beijing, May 2016]

ACADEMIC TRAVELLINGS

• The Annal Meeting of the Chinese Mathematical Society, Dalian University of Technology, Dalian, Dec. 23-25, 2023

• Winter Workshop on Number Theory, Wuhan University, Wuhan, Dec. 16-17, 2023

• Workshop on Number Theory, Huaiyin Normal University, Huaian, Nov. 11-12, 2023

• Workshop on Number Theory, Shandong University, Jinan, Oct. 14-15, 2023

• Satellite Conference in Number Theory of International Congress of Basic Science, Morningside Center of Mathematics, Beijing, Jul. 10-14, 2023

• Workshop on Number Theory and Applications, Xi'an Polytechnic University, Xi'an, May 20-22, 2023

• Mathematics Colloquium, Shanghai Jiao Tong University, Dec. 09, 2022 (online)

• Student Analytic Number Theory Seminar, Stanford University, Nov. 29/30, 2022 (online)

• Combinatorics, Linear Algebra and Number Theory Seminar, Washington State University, Nov. 29/30, 2022 (online)

• Number Theory Web Online Seminar, Sep. 08, 2022 (online)

• 2022 HKU Number Theory Days, The University of Hong Kong, Hong Kong, Jul. 18-29, 2022 (online)

• Pan Asian Number Theory Conference, Research Institute for Mathematical Sciences (RIMS), Kyoto, Dec. 06-10, 2021 (online)

• Workshop on Analytic and Combinatorial Number Theory, Shanghai Jiao Tong University, Oct. 30-31, 2021 (online)

• Workshop on Number Theory and Applications, Northwest University, Xi'an, Oct. 16-18, 2021

• The 9th East Asian Number Theory Conference, Okinawaken Seinenkaikan plus Zoom, Aug. 23-27, 2021

• 2021 International Conference on Number Theory, Sichuan University, Aug. 09-11, 2021 (online)

• The 8th National Conference on Number Theory, Jintan, Jun. 26-30, 2021

• Forum on Number Theory, Nanjing University, May 28-30, 2021

• Workshop on Algebra & Number Theory, Harbin Institute of Technology, Jun. 19-20, 2021

• Seminar on Number Theory & Arithmetic Geometry, Southern University of Science and Technology, May 22-23, 2021

• Symposium on Number Theory and Representation Theory, Zhejiang University, May 15-16, 2021

• Forum in Mathematics, Estern China Normal University, Mar. 20-22, 2021

• ICCM, University of Science and Technology of China, Dec. 27-29, 2020

• Online Conference on Number Theory and Applications, in honour of Chao Ko, Sichuan University, Nov. 21-23, 2020

• Westlake Number Theory Symposium 2020, Westlake University, Oct. 29-Nov. 01, 2020

• Workshop on Number Theory, Huaiyin Normal University, Oct. 24-25, 2020 (online)

• The 9th East Asian Number Theory Conference, Okinawaken Seinenkaikan, Aug. 24-27, 2020

• Pan Asian Number Theory Conference, Research Institute for Mathematical Sciences, Kyoto, Jul. 13-17, 2020

• The Sixth Southwest Conference on Number Theory, Chongqing Normal University, Chongqing, Dec. 13-15, 2019

• Workshop on Number Theory, China University of Mining and Technology, Beijing, Nov. 15-17, 2019

• Workshop on Analytic Number Theory, Harbin Institute of Technology, August 9-12, 2019

• 2019 HKU Number Theory Days, The University of Hong Kong, Hong Kong, Jul. 16-27, 2019

• Second Symposium on Analytic Number Theory, Grand Hotel San Michele, Cetraro, Italy, July 8-12, 2019

• Arithmetic, geometry, and modular forms: a conference in honour of Bill Duke, ETH Zürich, Zürich, Jun. 17-21, 2019

• Université Paris-Est Créteil, Créteil, May 6-May 9, 2019

• École Polytechnique Fédérale de Lausanne, Lausanne, Apr. 28-May 5, 2019

• Workshop on Number Theory, Nanjing Normal University, Nanjing, Mar. 30-31, 2019

• Winter School on Trace Functions And Their Applications, Congressi Stefano Franscini of ETH Zürich, Monte Verità, Jan. 14-18, 2019

• The Fifth Sichuan-Chongqing Workshop on Number Theory, Sichuan University, Chengdu, Dec. 15-17, 2018

• 2018 Workshop on Number Theory, Nanjing University, Nanjing, Oct. 26-28, 2018

• 2018 International Workshop on Analytic Number Theory and Diophantine Geometry, Shanghai University, Shanghai, Oct. 20-21, 2018

• Seminar on Analytic Number Theory, Chinese Academy of Sciences, Beijing, Sep. 15/16, Oct. 13/14, 2018

• 2018 HKU Number Theory Days, The University of Hong Kong, Hong Kong, Jul. 16-23, 2018

• Dynamics: Topology and Numbers, Max Planck Institute for Mathematics, Bonn, Jul.02-06, 2018

• Hausdorff School: L-functions: Open Problems and Current Methods, Hausdorff Center for Mathematics, Bonn, Jun. 25-29, 2018

• Automorphic Forms and L-Functions, Shandong University, Qingdao Campus, Qingdao, Jun. 18-22, 2018

• Westlake Seminar on Number Theory, Westlake Institute for Advanced Study, Hangzhou, Nov. 25-26/Dec. 16-17, 2017

• Seminar on Analytic Number Theory, Chinese Academy of Sciences, Beijing, Oct. 14/15/28/29, 2017

• Hangzhou Number Theory Conference, Zhejiang University, Hangzhou, Sep. 22-24, 2017

• Seminar on Number Theory and Operator Algebra, Chinese Academy of Sciences, Beijing, Aug. 15-18, 2017

• The University of Hong Kong, Jul. 01-13, 2017

• Program on Analytic Number Theory, MSRI, Berkeley, Feb. 01-20, May 01-19, 2017

• Seminar on Analytic Number Theory, Chinese Academy of Sciences, Beijing, Apr. 08/09/22/23, 2017

• Workshop on Analytic Number Theory and Cryptography, China University of Mining and Technology, Beijing, Nov. 18-20, 2016

• Seminar on Analytic Number Theory, Chinese Academy of Sciences, Beijing, Oct. 15/16/29/30, 2016

• École Polytechnique Fédérale de Lausanne, Lausanne, Oct. 01-09, 2016

• Université de Lorraine, Nancy, Sep. 18-30, 2016

• ICCM 2016, Chinese Academy of Sciences, Beijing, Jul. 05-11, 2016

• Workshop on Number Theory and Applications, Northwest University, Xi'an, Jun. 25-26, 2016

• Seminar on Analytic Number Theory, Chinese Academy of Sciences, Beijing, May 14/15/28/29, 2016

• Workshop on Analytic Number Theory, Shanghai Jiao Tong University, Shanghai, Nov. 28-29, 2015

• Chinese-Russian Workshop on Exponential Sums and Sumsets, Chinese Academy of Sciences, Beijing, Nov. 05-14, 2015 

• Yu.V. Linnik Centennial Conference: Analytical Methods in Number Theory, Probability Theory and Mathematical Statistics, EIMI, St. Petersburg, Sep. 14-18, 2015

• 2015 Workshop on Number Theory, MCM, Beijing, Jul. 16-31, 2015 

• The 7th National Conference on Number Theory, Shandong University, Jinan, May 16-19, 2015

• Nicholas Katz's 71st Birthday Conference on Arithmetic Algebraic Geometry, MCM, Beijing, May 11-15, 2015

• Ergodic Prime Number Theorems Seminar 2015, MCM, Beijing, Mar. 28-May 31, 2015

• Workshop on Number Theory and Applications, Northwest University, Xi'an, Oct. 24-28, 2014

• École d’été: Théorie Analytique des Nombres, IHÉS, Bures-sur-Yvette, Jul. 09-23, 2014

• Number Theory Days (11th Edition) 2014, ETHZ, Zürich, Mar. 07-08, 2014

• Automorphic Forms and Arithmetic, Georg-August-Universität Göttingen, Göttingen, Feb. 09-14, 2014

• Étienne Fouvry 60th Birthday Conference on Analytic Number Theory, CIRM, Luminy, Jul. 17-21, 2013

• Arithmetics & Geometry: 25 Years Number Theory Seminar, ETHZ, Zürich, Jun. 03-07, 2013

• Equidistribution in Number Theory and Dynamics, ETHZ, Zürich, Mar. 18-22, 2013

• Number Theory Days (10th Edition) 2013, EPFL, Lausanne, Mar. 15-16, 2013

• Arithmetic of Abelian Varieties in Families, EPFL, Lausanne, Nov. 12-16, 2012

• China-France Summer School on Number Theory, Shandong University, Weihai, Jul. 16-25, 2012

• Ergodic Prime Number Theorems Seminar 2012, MCM, Beijing, Mar. 31 - Jun. 02, 2012

• One-Day Workshop on Analytic Number Theory, China University of Mining and Technology, Beijing, Mar. 24, 2012

• 2011 International Conference on Number Theory, Shanghai Jiao Tong University, Shanghai, Aug. 15-17, 2011

• Workshop on Number Theory, Northwest University, Xi'an, Jun. 19-26, 2011

• CIMPA Research School on Automorphic Forms and L-Functions, Shandong University, Weihai, Aug. 01-14, 2010

• National Conference on Number Theory, Chern Institute of Mathematics, Tianjin, Aug. 23-28, 2009

• International Conference on Number Theory and Representation Theory, Shandong University, Weihai, Aug. 02-08, 2009