Kannan Soundararajan

All Publications

• The distribution of consecutive prime biases and sums of sawtooth random variables MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY Oliver, R., Soundararajan, K. 2020; 168 (1): 149–69

  View details for DOI 10.1017/S0305004118000592

  View details for Web of Science ID 000503104600008

• THE MEAN SQUARE OF THE PRODUCT OF A DIRICHLET L-FUNCTION AND A DIRICHLET POLYNOMIAL FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Conrey, B., Iwaniec, H., Soundararajan, K. 2019; 61 (2): 147–77

  View details for DOI 10.7169/facm/1767

  View details for Web of Science ID 000502977700002

• WEAK SUBCONVEXITY WITHOUT A RAMANUJAN HYPOTHESIS DUKE MATHEMATICAL JOURNAL Soundararajan, K., Thorner, J., Brumley, F. 2019; 168 (7): 1231–68

  View details for DOI 10.1215/00127094-2018-0065

  View details for Web of Science ID 000468608500002

• Maximum of the Riemann Zeta Function on a Short Interval of the Critical Line COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS Arguin, L., Belius, D., Bourgade, P., Radziwill, M., Soundararajan, K. 2019; 72 (3): 500–535

  View details for DOI 10.1002/cpa.21791

  View details for Web of Science ID 000456056100002

• Fourier optimization and prime gaps COMMENTARII MATHEMATICI HELVETICI Carneiro, E., Milinovich, M. B., Soundararajan, K. 2019; 94 (3): 533–68

  View details for DOI 10.4171/CMH/467

  View details for Web of Science ID 000487814300004

• A MORE INTUITIVE PROOF OF A SHARP VERSION OF HALASZ'S THEOREM PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Granville, A., Harper, A. J., Soundararajan, K. 2018; 146 (10): 4099–4104

  View details for DOI 10.1090/proc/14095

  View details for Web of Science ID 000440342000002

• The variance of divisor sums in arithmetic progressions FORUM MATHEMATICUM Rodgers, B., Soundararajan, K. 2018; 30 (2): 269–93

  View details for DOI 10.1515/forum-2016-0227

  View details for Web of Science ID 000426251100001

• Nonzero coefficients of half-integral weight modular forms mod l RESEARCH IN THE MATHEMATICAL SCIENCES Bellaiche, J., Green, B., Soundararajan, K. 2018; 5

  View details for DOI 10.1007/s40687-018-0123-7

  View details for Web of Science ID 000451385100001

• Large character sums: Burgess's theorem and zeros of L-functions JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY Granville, A., Soundararajan, K. 2018; 20 (1): 1–14

  View details for DOI 10.4171/JEMS/757

  View details for Web of Science ID 000423690700001

• 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

  View details for DOI 10.1093/qmath/haw005

  View details for Web of Science ID 000399764800005

• 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

  View details for Web of Science ID 000393926100013

• Selberg's central limit theorem for log vertical bar zeta(1/2 ENSEIGNEMENT MATHEMATIQUE Radziwill, M., Soundararajan, K. 2017; 63 (1-2): 1–19

  View details for DOI 10.4171/LEM/63-1/2-1

  View details for Web of Science ID 000437158200001

• 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

  View details for DOI 10.1007/s00222-015-0582-z

  View details for Web of Science ID 000365282600003

• 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

  View details for Web of Science ID 000369811000013

• The number of nonzero coefficients of modular forms (mod p) ALGEBRA & NUMBER THEORY Bellaiche, J., Soundararajan, K. 2015; 9 (8): 1825-1856

  View details for DOI 10.2140/ant.2015.9.1825

  View details for Web of Science ID 000365543300003

• Carries, Group Theory, and Additive Combinatorics AMERICAN MATHEMATICAL MONTHLY Diaconis, P., Shao, X., Soundararajan, K. 2014; 121 (8): 674-688

  View details for DOI 10.4169/amer.math.monthly.121.08.674

  View details for Web of Science ID 000343376800002

• Critical zeros of Dirichlet L-functions JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Conrey, J. B., Iwaniec, H., Soundararajan, K. 2013; 681: 175-198

  View details for DOI 10.1515/crelle-2012-0032

  View details for Web of Science ID 000322973600007

• A generalization of the Plya-Vinogradov inequality RAMANUJAN JOURNAL Frolenkov, D. A., Soundararajan, K. 2013; 31 (3): 271-279

  View details for DOI 10.1007/s11139-012-9462-y

  View details for Web of Science ID 000322744200003

• The prime geodesic theorem JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Soundararajan, K., Young, M. P. 2013; 676: 105-120

  View details for DOI 10.1515/crelle.2012.002

  View details for Web of Science ID 000315592500005

• CONTINUOUS LOWER BOUNDS FOR MOMENTS OF ZETA AND L-FUNCTIONS MATHEMATIKA Radziwill, M., Soundararajan, K. 2013; 59 (1): 119-128

  View details for DOI 10.1112/S0025579312001088

  View details for Web of Science ID 000327271600007

• An asymptotic expansion related to the Dickman function RAMANUJAN JOURNAL Soundararajan, K. 2012; 29 (1-3): 25-30

  View details for DOI 10.1007/s11139-011-9304-3

  View details for Web of Science ID 000310975300003

• The Sixth Power Moment of Dirichlet L-Functions GEOMETRIC AND FUNCTIONAL ANALYSIS Conrey, J. B., Iwaniec, H., Soundararajan, K. 2012; 22 (5): 1257-1288

  View details for DOI 10.1007/s00039-012-0191-6

  View details for Web of Science ID 000310426000006

• 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

  View details for DOI 10.1112/plms/pdr037

  View details for Web of Science ID 000302491400004

• Random Multiplicative Functions in Short Intervals INTERNATIONAL MATHEMATICS RESEARCH NOTICES Chatterjee, S., Soundararajan, K. 2012: 479-492

  View details for DOI 10.1093/imrn/rnr023

  View details for Web of Science ID 000300038500001

• 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

  View details for DOI 10.1112/blms/bdq095

  View details for Web of Science ID 000288567300002

• 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

  View details for Web of Science ID 000208775400013

• On modular signs MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY Kowalski, E., Lau, Y., Soundararajan, K., Wu, J. 2010; 149: 389-411

  View details for DOI 10.1017/S030500411000040X

  View details for Web of Science ID 000283812700002

• Weak subconvexity for central values of L-functions ANNALS OF MATHEMATICS Soundararajan, K. 2010; 172 (2): 1469-1498

  View details for Web of Science ID 000282059600016

• Mass equidistribution for Hecke eigenforms ANNALS OF MATHEMATICS Holowinsky, R., Soundararajan, K. 2010; 172 (2): 1517-1528

  View details for Web of Science ID 000282059600018

• Quantum unique ergodicity for SL2(Z)\H ANNALS OF MATHEMATICS Soundararajan, K. 2010; 172 (2): 1529-1538

  View details for Web of Science ID 000282059600019

• Fixed Points for Discrete Logarithms 9th International Symposium on Algorithmic Number Theory Levin, M., Pomerance, C., Soundararajan, K. SPRINGER-VERLAG BERLIN. 2010: 6–15

  View details for Web of Science ID 000286148700005

• 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

• Moments of the Riemann zeta function ANNALS OF MATHEMATICS Soundararajan, K. 2009; 170 (2): 981-993

  View details for Web of Science ID 000271956100017

• Partial sums of the Mobius function JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Soundararajan, K. 2009; 631: 141-152

  View details for DOI 10.1515/CRELLE.2009.044

  View details for Web of Science ID 000268734100005

• 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

  View details for DOI 10.1007/s00208-008-0280-x

  View details for Web of Science ID 000263062700001

• Extreme values of zeta and L-functions MATHEMATISCHE ANNALEN Soundararajan, K. 2008; 342 (2): 467-486

  View details for DOI 10.1007/s00208-008-0243-2

  View details for Web of Science ID 000258718200013

• The distribution of smooth numbers in arithmetic progressions CRM Workshop on the Anatomy of Integers Soundararajan, K. AMER MATHEMATICAL SOC. 2008: 115–128

  View details for Web of Science ID 000258329200008

• 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

  View details for Web of Science ID 000258329200015

• An uncertainty principle for arithmetic sequences ANNALS OF MATHEMATICS Granville, A., Soundararajan, K. 2007; 165 (2): 593-635

  View details for Web of Science ID 000248552700006

• 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

  View details for DOI 10.1112/S0024610706023131

  View details for Web of Science ID 000242433500002