Welcome to Research Center for Mathematics and Interdisciplinary Sciences (Frontiers Science Center for Nonlinear Expectations)!

Jianya LIU

Professor

Vice principal

Shandong University



RESEARCH GRANTS

2016-2020: Key project ''automorphic representations and the arithmetic of algebraic varieties'', by the National Natural Science Foundation
2011-2014: Key project ''the arithmetic and geometry of automorphic forms'', by the National Natural Science Foundation
2006-2008: Key project ''the arithmetic and geometry of automorphic forms'', by the National Natural Science Foundation
2005-2007: Major grant program for sciences and technology, by the Ministry of Education
2002-2005: National science foundation for distinguished young scholars, by the National Natural Science Foundation
2001-2003: Trans-Century training program foundation for the talents, by the Ministry of Education


CONFERENCES ORGANISED

[10] May 16-19, 2015, The 7th National Conference on Number Theory, Shandong University, Jinan
[9] Aug. 1-14, 2010,
CIMPA Research School on Automorphic forms and L-functions, Weihai Campus, Shandong University, Weihai
[8] Aug. 2-8, 2009,
International Conference on Number Theory and Representation Theory, Weihai Campus, Shandong University, Weihai
[7] Aug. 16-26, 2008,
Workshop on Additive Number Theory, Weihai Campus, Shandong University, Weihai
[6] Aug. 1-Sep. 3, 2007,
Summer School on Arithmetic, School of Mathematics, Shandong University
[5] Aug. 30-Sep. 3, 2006, The Fourth China-Japan Conference on Number      Theory, Weihai Campus, Shandong University, Weihai
[4] Dec. 20-22, 2005, Workshop on Number Theory and Applications(In Memory of Professor Chengdong Pan, Shandong University, Jinan
[3] Aug. 1-14, 2005, International Summer School on Analytic Number Theory, Center of Mathematical Sciences, Zhejiang University, Hangzhou.
[2] Aug. 2004, The 9th National Summer School in Mathematics, Weihai Campus, Shandong University, Weihai
[1] Aug. 13-17, 2002, ICM2002, Satellite conference Number Theory and Arith-metic Geometry, Weihai Campus, Shandong University, Weihai


INVITED TALKS

[39] Nov. 21-25, 2015, Annual Meeting of the Chinese Mathematical Society.
[38] Sep. 1 - 9 2012,
Synergies and Vistas in Analytic Number Theory, University of Oxford
[37] Jun. 16 – 25 2012, The International conference on Number Theory, The University of Hongkong??
[36] Jun. 3 - 8 2012, Analytic Methods for Diophantine Problems, University of Goettingen, Germany
[35] Apr. 30 – May 16 2012, Interactions Between Ergodic Theory, Number Theory and Noncommutative Geometry, The Ohio State University
[34] Aug. 28 - Sep. 3 2011, The Analytic Theory of Automorphic Forms, Mathematisches Forschungsinstitut Oberwolfach, Germany
[33] Jan. 19 - Jun. 1 2011, Ecole Polytechnique federale de Lausanne, Switzerland
[32] Sep. 12 - 18 2010, The Second Pan-Asian Number Theory Confernce, Kyoto University, Japan
[31] Jan. 8-11, 2009,
Pan Asia Number Theory, POSTECH, Pohang, Korea
[30] Dec. 6-13, 2008, Colloquium, The University of Iowa, USA
[29] Aug. 30-Sep. 3, 2008, The Fifth China-Japan Conference on Number Theory,  Kinki University, Japan
[28] Mar. 9-15, 2008,
Workshop on Analytic Number Theory, Mathematisches Forschungsinstitut Oberwolfach, Germany
[27] Jan. 21-24, 2008, East Asia Number Theory Conference, KAIST Korea

      Title: Prime Solutions to Quadratic Equations

[26] Dec. 17-22, 2007, The Fourth International Congress of Chinese Mathematicians, Zhejiang University, China
      Title: Primes on Orbits
[25] Jul. 6-8, 2007, Conference on Representation Theory and L-functions, The University of Iowa, Iowa City
      Title: Representation of integers by squares of primes
[24] Jun. 28, 2007, Universite de Nancy I, France
      Title: Almost primes on orbits
[23] Apr. 23-May 11, 2007, School and Conference on Analytic Number Theory, ICTP, Italy
      Title: Distribution of primes on orbits (With P. Sarnak)
[22] Mar. 25, 2007, School on automorphic forms, POSTECH, Korea
      Title: Lectures on Masss Forms
[21] Jan. 29, 2007, The International Conference, Analytic Problems in Number Theory, The 100th anniversary of A. O. Gelfond, Moscow Lomonosov State University
      Title: The second barrier for automorphic L-functions on the critical line
[20] Nov., 2006, School of Mathematics, Institute for Advanced Study
      Title: A Weyl-like bound for automorphic L-functions
[19] Oct., 2006, Department of Mathematics, University of Wisconsin at Madison
      Title: Rankin-Selberg L-functions
[18] Oct., 2006, International Conference on Subconvexity bounds for L-functions, American Institute of Mathematics, Palo Alto
      Title: Subconvexity bounds for Automorphic L-functions
[17] Apr.-Jun., 2006, Department of Mathematics, Princeton University
      Title: Subconvexity for L-functions
[16] Apr., 2006, Department of Mathematics, Johns Hopkins University
      Title: A Weyl-like bound for automorphic L-functions
[15] Nov., 2005, Annual Meeting of Japan Number Theory, Kinki University
[14] Oct., 2005, Department of Mathematics, Nagoya University, Japan
      Title: Selberg’s orthogonality conjecture for automorphic L-functions
[13] Aug. 11-16, 2005, International Conference on Arithmetic Geometry and Automorphic Forms, Nankai University, Tianjin
      Title: A subconvexity bound for Rankin-Selberg L-functions
[12] Nov., 2004, International Conference In Memory of Professor Chudakov's  100th Birthday, Moscow State University
      Title: An iterative method in the Waring-Goldbach problem
[11] Oct., 2004, International Conference on Number Theory and Applications, Kyoto University, Japan
[10] Apr., 2004, Universite de Nancy I, France
    Title: Subconvexity bounds of automorphic L-functions
[9] Apr., 2004, Universite de Bordeaux I, France
    Title: Subconvexity bounds of automorphic L-functions
[8] Feb. 12-14, 2004, The third China-Japan Conference on Number Theory, Northwest University, Xi'an
[7] Oct. 8, 2003, Johns Hopkins Universtiy, USA
    Title: Subconvexity for Rankin-Selberg L-functions
[6] 2000, International Conference In Memory of Professor Loo-Keng Hua's 90th Birthday, Beijing
    Title: Binary and almost binary problems
[5] Jan.-Jun., 2000, Lie Group Programme, The University of Hong Kong
    Title: Introduction to the spectral theory of automorphic forms
[4] 2000, International Conference In Memory of Professor Zhao Ke's 90th Birthday, Sichuan University, Chengdu
    Title: Additive problems on squares of primes
[3] Jun., 1999, The First China-Japan Conference on Number Theory, Beijing
    Title: Sums of squares
[2] 1998, Annual Meeting of Hong Kong Mathematical Society, The University of Hong Kong
    Title: Sums of squares
[1] Dec. 1998-Jun. 1999, Lie Group Programme, The University of Hong Kong
    Title: Automorphic forms on SL(2, R)


PUBLICATIONS

[65] (with Sarnak, Peter) The Möbius function and distal flows. Duke Math.  J. 164  (2015), no. 7, 1353–1399.
[64] (with Wu, Jie) The number of coefficients of automorphic L-functions  for GL(m) of same signs. J. Number Theory 148 (2015), 429–450.
 [63] (with Lau, Yuk-Kam; Wu, Jie) Sign changes of the coefficients of  automorphic L-functions. Number theory; arithmetic in Shangri-La, 141–181, Ser.  Number       Theory Appl., 8, World Sci. Publ., Hackensack, NJ, 2013.
[62] (with Lau Yuk-Kam and Wu Jie)The first negative coefficients of symmetric square L-functions, Ramanujan J (2012) 27:419–441
[61] Enlarged Major Arcs in Additive Problems. II, Proceedings of the Steklov Institute of Mathematics, 2012, Vol. 276, pp. 176–192
[60] (with Qu, Yan; Wu, Jie) Two Linnik-type problems for automorphic L-functions,  Math. Proc. Cambridge Philos. Soc. 151 (2011), no. 2, 219–227.
[59] Integral points on quadrics with prime coordinates, Monatsh. Math. 164 (2011), no. 4, 439–465.
[58] A quick introduction to Maass forms. Number theory, 184–216, Ser. Number Theory Appl., 6, World Sci. Publ., Hackensack, NJ, 2010.
[57] Enlarged Major Arcs in Additive Problems, Mathematical Notes, 88 (2010), 395-401.
[56] (with P. Sarnak) Integral points on quadrics in three variables whose coordinates have few prime factors, Israel J. of math., 178 (2010), 393–426.
[55] (with Lau Yuk-Kam and Wu Jie) Coefficients of symmetric square L-functions, Sci China Math, 2010, 53, doi: 10.1007/s11425-010-4046-z.
[54] (with J. Brudern, R. Dietmann and T. D. Wooley) A Birch–Goldbach theorem,  Arch. Math. 94 (2010), 53–58.
[53] (with A. V. Kumchev) Sums of primes and squares of primes in short intervals,  Monatsh. Math. (2009) 157, 335-363.
[52] (with Y. Wang) A theorem on analytic strong multiplicity one, J. Number Theory 129 (2009) No. 8 1874-1882.
[51] (with Y. Ye) Functoriality of automorphic L-functions through their zeros, Sci. China Ser. A, 52 (2009), 1-16.
[50] (with Y. Ye) Correlation of zeros of automorphic L-functions, Sci. China Ser. A, 51 (2008), 1147-1166.
[49] (with E. Royer and J. Wu) On a conjeture of Montgomery-Vaughan on extreme values of automorphic L-functions at 1, Centre de Recherches Mathematiques, CRM Proceedings and Lecture Notes, 46 (2008).
[48] (with Y. Ye) Perron's formula and the prime number theorem for automor- phic L-functions, Pure Appl. Math. Q., 3 (2007), 481-497.
[47] A large sieve estimate for Dirichlet polynomials and  its applications, Ann. Univ. Sci. Budapest., Sect. Comp., 27 (2007), 91-110.
[46] (with T. Zhan) The quadratic Waring-Goldbach problem, J. Shandong Univ., 42(2) (2007), 1-18.
[45] (with Y.-K. Lau, Y. Ye) Shifted convolution sums of Fourier coefficients of cusp forms, Number theory, 108--135, Ser. Number Theory Appl., 2, World Sci. Publ., Hackensack, NJ, 2007.
[44] (with Y. Ye) Petersson and Kuznetsov trace formulas, Lie groups and auto- morphic forms, 147-168, AMS/IP Stud. Adv. Math., 37, Amer. Math. Soc., Providence, RI, 2006.
[43] (with Y. Ye) Zeros of automorphic L-functions and noncyclic base change, Number theory, 119-152, Dev. Math., 15, Springer, New York, 2006.
[42] (with G. Lü, T. Zhan) Exponential sums over primes in short intervals, Sci. China Ser. A, 49 (2006), 611-619.
[41](with Y. K. Lau, Y. Ye) Subconvexity bounds for Rankin-Selberg L-functions for congruence subgroups, J. Number Theory., 121 (2006), 204-223.
[40] (with Y.-K. Lau, Y. Ye) A new bound k^{2/3+\epsilon} for Rankin-Selberg L-functions for Hecke congruence subgroups, Int. Math. Res.Pap.,2006, 1-78.
[39] (with J. Ye) Mean-value estimates for nonlinear Weyl sums  over primes, Japan. J. Math. (N.S.), 31  (2005), 379-390.
[38] (with Y. Wang, Y. Ye) A proof of Selberg's orthogonality for automorphic L-functions, Manuscripta Math., 118 (2005), 135-149.
[37] An iterative method in the Waring-Goldbach problem, Chebyshevskii Sb., 5 (2005), 164-179.
[36] (with K.-M. Tsang) Small prime solutions of ternary linear equations,  Acta  Arith., 118 (2005), 79-100.
[35] (with T. Zhan) The exceptional set in Hua's theorem for three squares of primes, Acta Math. Sin. (Engl. Ser.), 21 (2005), 335-350.
[34] (with Y. Ye) Selberg's orthogonality conjecture for automorphic L-functions,  Amer. J. Math., 127 (2005), 837-849.
[33] (with Y. Ye) Weighted Selberg orthogonality and uniqueness of factorization of automorphic L-functions, Forum Math., 17 (2005), 493-512.
[32] (with Y. Ye) Distribution of zeros of Dirichlet L-functions and the least prime in  an arithmetic progression, Acta Arith., 119 (2005), 13-38.
[31] (with K.K. Choi) Small prime solutions of quadratic equations II, Proc. Amer. Math. Soc., 133 (2005), 945-951.
[30] (with T.D. Wooley and G. Yu) The quadratic Waring-Goldbach problem, J. Number Theory, 107 (2004), 298-321.
[29] (with G. Lü) Four squares of primes and 165 powers of 2, Acta Arith., 114       (2004), 55-70.
[28] On Lagrange's theorem with prime variables, Q. J. Math., 54 (2003), 453-
462.
[27] (with Y. Ye) Subconvexity for Rankin-Selberg L-functions of Maass forms, Geom. Funct. Anal., 12 (2002), 1296-1323.
[26] (with Y. Ye) Superposition of zeros of distinct L-functions, Forum Math., 14 (2002), 419-455.
[25] (with M.-C. Liu and T. Zhan) Squares of primes and powers of 2. II, J. Num- ber Theory, 92 (2002), 99-116.
[24] (with K.K. Choi) Small prime solutions of quadratic equations, Canad. J. Math., 54 (2002), 71-91.
[23] (with Y. Ye) The pair correlation of zeros of the Riemann zeta function and distribution of primes, Arch. Math. (Basel), 76 (2001), 41-50.
[22] (with T. Zhan) Distribution of integers that are sums of three squares of primes, Acta Arith., 98 (2001), 207-228.
[21] (with T. Zhan) Hua's theorem on prime squares in short intervals, Acta Math.  Sin. (Engl. Ser.), 16 (2000), 669-690.
[20] (with M.-C. Liu) The exceptional set in the four prime squares problem, Illinois J. Math., 44 (2000), 272-293.
[19] (with M.-C. Liu) Representation of even integers as sums of squares of primes and powers of 2, J. Number Theory, 83 (2000), 202-225.
[18] (with M.-C. Liu and T. Zhan) Squares of primes and powers of 2, Monatsh. Math., 128 (1999), 283-313.
[17] (with M.-C. Liu and T.Z. Wang) On the almost Goldbach problem of Linnik, Les XXèmes Journées Arithmétiques (Limoges, 1997). J. Théor. Nombres Bordeaux, 11 (1999), 133-147.
[16] (with T. Zhan) The Goldbach-Vinogradov theorem, Number theory in progress,  2 (Zakopane-Koscielisko, 1997), 1005-1023, de Gruyter, 1999.
[15] (with M.-C. Liu and T.Z. Wang) The number of powers of 2 in a representa- tion of large even integers. II, Sci. China Ser. A, 41 (1998), 1255-1271.
[14] The Goldbach-Vinogradov theorem with three primes in a thin subset, Chinese Ann. Math. Ser. B, 19 (1998), 479-488.
[13] (with M.-C. Liu and T.Z. Wang) The number of powers of 2 in a representa- tion of large even integers. I, Sci. China Ser. A, 41 (1998), 386-398.
[12] (with T. Zhan) Exponential sums involving the Mobius function, Indag. Math. (N.S.), 7 (1996), 271-278.
[11] (with T. Zhan) Estimation of exponential sums over primes in short intervals  I, Monatsh. Math., 127 (1999), 27-41.
[10] (with T. Zhan) Sums of five almost equal prime squares. II, Sci. China Ser. A, 41 (1998), 710-722.
[9] (with T. Zhan) On a theorem of Hua, Arch. Math. (Basel), 69 (1997), 375-390.
[8] (with T. Zhan) The ternary Goldbach problem in arithmetic progressions, Acta Arith., 82 (1997), 197-227.
[7] (with T. Zhan) Estimation of exponential sums over primes in short intervals. II, Analytic number theory, 2 (Allerton Park, IL, 1995), 571-606, Progr. Math.,      139, Birkhauser Boston, Boston, MA, 1996.
[6] On an error term of Chowla. III, J. Number Theory, 64 (1997), 51-58.
[5] On an error term of Chowla. II, J. Number Theory, 64 (1997), 36-50.
[4] On an error term of Chowla. I, J. Number Theory, 64 (1997), 20-35.
[3] (with T.Zhan) A Bombieri-type mean-value theorem concerning exponential sums over primes, Chinese Sci. Bull., 41 (1996), 363-366.
[2] (with T. Zhan) On sums of five almost equal prime squares, Acta Arith., 77 (1996), 369-383.
[1] Remark on a theorem of Wolke, Arch. Math. (Basel), 65 (1995), 413-416.