Academic Appointments


  • Professor, Mathematics

2018-19 Courses


Stanford Advisees


  • Doctoral Dissertation Advisor (AC)
    Vivian Kuperberg, Sarah Peluse

All Publications


  • CORRIGENDUM TO "CONDITIONAL BOUNDS FOR THE LEAST QUADRATIC NON-RESIDUE AND RELATED PROBLEMS" MATHEMATICS OF COMPUTATION Lamzouri, Y., Li, X., Soundararajan, K. 2017; 86 (307): 2551-2554

    View details for DOI 10.1090/mcom/3261

    View details for Web of Science ID 000400929100023

  • LOWER BOUNDS FOR THE VARIANCE OF SEQUENCES IN ARITHMETIC PROGRESSIONS: PRIMES AND DIVISOR FUNCTIONS QUARTERLY JOURNAL OF MATHEMATICS Harper, A. J., Soundararajan, K. 2017; 68 (1): 97-123
  • ON SHORT SUMS OF TRACE FUNCTIONS ANNALES DE L INSTITUT FOURIER Fouvry, E., Kowalski, E., Michel, P., Raju, C. S., Rivat, J., Soundararajan, K. 2017; 67 (1): 423-449
  • Unexpected biases in the distribution of consecutive primes. Proceedings of the National Academy of Sciences of the United States of America Lemke Oliver, R. J., Soundararajan, K. 2016; 113 (31): E4446-54

    Abstract

    Although the sequence of primes is very well distributed in the reduced residue classes [Formula: see text], the distribution of pairs of consecutive primes among the permissible ϕ(q)(2) pairs of reduced residue classes [Formula: see text] is surprisingly erratic. This paper proposes a conjectural explanation for this phenomenon, based on the Hardy-Littlewood conjectures. The conjectures are then compared with numerical data, and the observed fit is very good.

    View details for DOI 10.1073/pnas.1605366113

    View details for PubMedID 27418603

    View details for PubMedCentralID PMC4978288

  • Riemann hypothesis for period polynomials of modular forms. Proceedings of the National Academy of Sciences of the United States of America Jin, S., Ma, W., Ono, K., Soundararajan, K. 2016; 113 (10): 2603-2608

    Abstract

    The period polynomial [Formula: see text] for an even weight [Formula: see text] newform [Formula: see text] is the generating function for the critical values of [Formula: see text]. It has a functional equation relating [Formula: see text] to [Formula: see text]. We prove the Riemann hypothesis for these polynomials: that the zeros of [Formula: see text] lie on the circle [Formula: see text]. We prove that these zeros are equidistributed when either k or N is large.

    View details for DOI 10.1073/pnas.1600569113

    View details for PubMedID 26903628

    View details for PubMedCentralID PMC4790983

  • Moments and distribution of central L-values of quadratic twists of elliptic curves INVENTIONES MATHEMATICAE Radziwill, M., Soundararajan, K. 2015; 202 (3): 1029-1068
  • CONDITIONAL BOUNDS FOR THE LEAST QUADRATIC NON-RESIDUE AND RELATED PROBLEMS MATHEMATICS OF COMPUTATION Lamzouri, Y., Li, X., Soundararajan, K. 2015; 84 (295): 2391-2412
  • The number of nonzero coefficients of modular forms (mod p) ALGEBRA & NUMBER THEORY Bellaiche, J., Soundararajan, K. 2015; 9 (8): 1825-1856
  • Carries, Group Theory, and Additive Combinatorics AMERICAN MATHEMATICAL MONTHLY Diaconis, P., Shao, X., Soundararajan, K. 2014; 121 (8): 674-688
  • Critical zeros of Dirichlet L-functions JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Conrey, J. B., Iwaniec, H., Soundararajan, K. 2013; 681: 175-198
  • A generalization of the Plya-Vinogradov inequality RAMANUJAN JOURNAL Frolenkov, D. A., Soundararajan, K. 2013; 31 (3): 271-279
  • The prime geodesic theorem JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Soundararajan, K., Young, M. P. 2013; 676: 105-120
  • CONTINUOUS LOWER BOUNDS FOR MOMENTS OF ZETA AND L-FUNCTIONS MATHEMATIKA Radziwill, M., Soundararajan, K. 2013; 59 (1): 119-128
  • An asymptotic expansion related to the Dickman function RAMANUJAN JOURNAL Soundararajan, K. 2012; 29 (1-3): 25-30
  • The Sixth Power Moment of Dirichlet L-Functions GEOMETRIC AND FUNCTIONAL ANALYSIS Conrey, J. B., Iwaniec, H., Soundararajan, K. 2012; 22 (5): 1257-1288
  • Counting smooth solutions to the equation A plus B=C PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY Lagarias, J. C., Soundararajan, K. 2012; 104: 770-798
  • Random Multiplicative Functions in Short Intervals INTERNATIONAL MATHEMATICS RESEARCH NOTICES Chatterjee, S., Soundararajan, K. 2012: 479-492
  • Small gaps between zeros of twisted L-functions ACTA ARITHMETICA Conrey, J. B., Iwaniec, H., Soundararajan, K. 2012; 155 (4): 353-371

    View details for DOI 10.4064/aa155-4-2

    View details for Web of Science ID 000313309300002

  • A RULE OF THUMB FOR RIFFLE SHUFFLING ANNALS OF APPLIED PROBABILITY Assaf, S., Diaconis, P., Soundararajan, K. 2011; 21 (3): 843-875

    View details for DOI 10.1214/10-AAP701

    View details for Web of Science ID 000291736600002

  • Bounding vertical bar zeta(1/2+it)vertical bar on the Riemann hypothesis BULLETIN OF THE LONDON MATHEMATICAL SOCIETY Chandee, V., Soundararajan, K. 2011; 43: 243-250
  • Smooth solutions to the abc equation: the xyz Conjecture JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX Lagarias, J. C., Soundararajan, K. 2011; 23 (1): 209-234
  • On modular signs MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY Kowalski, E., Lau, Y., Soundararajan, K., Wu, J. 2010; 149: 389-411
  • Weak subconvexity for central values of L-functions ANNALS OF MATHEMATICS Soundararajan, K. 2010; 172 (2): 1469-1498
  • Quantum unique ergodicity for SL2(Z)\H ANNALS OF MATHEMATICS Soundararajan, K. 2010; 172 (2): 1529-1538
  • Mass equidistribution for Hecke eigenforms ANNALS OF MATHEMATICS Holowinsky, R., Soundararajan, K. 2010; 172 (2): 1517-1528
  • The second moment of quadratic twists of modular L-functions JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY Soundararajan, K., Young, M. P. 2010; 12 (5): 1097-1116

    View details for DOI 10.4171/JEMS/224

    View details for Web of Science ID 000281955400002

  • Fixed Points for Discrete Logarithms 9th International Symposium on Algorithmic Number Theory Levin, M., Pomerance, C., Soundararajan, K. SPRINGER-VERLAG BERLIN. 2010: 6–15
  • Moments of the Riemann zeta function ANNALS OF MATHEMATICS Soundararajan, K. 2009; 170 (2): 981-993
  • Partial sums of the Mobius function JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Soundararajan, K. 2009; 631: 141-152
  • On the distribution of imaginary parts of zeros of the Riemann zeta function, II MATHEMATISCHE ANNALEN Ford, K., Soundararajan, K., Zaharescu, A. 2009; 343 (3): 487-505
  • Extreme values of zeta and L-functions MATHEMATISCHE ANNALEN Soundararajan, K. 2008; 342 (2): 467-486
  • The distribution of smooth numbers in arithmetic progressions CRM Workshop on the Anatomy of Integers Soundararajan, K. AMER MATHEMATICAL SOC. 2008: 115–128
  • Pretentious multiplicative functions and an inequality for the zeta-function CRM Workshop on the Anatomy of Integers Granville, A., Soundararajan, K. AMER MATHEMATICAL SOC. 2008: 191–197
  • An uncertainty principle for arithmetic sequences ANNALS OF MATHEMATICS Granville, A., Soundararajan, K. 2007; 165 (2): 593-635
  • Benford's law for the 3 alpha+1 function JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES Lagarias, J. C., Soundararajan, K. 2006; 74: 289-303