Kannan Soundararajan

All Publications

• A supplement to Chebotarev's density theorem SCIENCE CHINA-MATHEMATICS Harcos, G., Soundararajan, K. 2023

  View details for DOI 10.1007/s11425-022-2141-1

  View details for Web of Science ID 001020258600001

• Almost all entries in the character table of the symmetric group are multiples of any given prime JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Peluse, S., Soundararajan, K. 2022

  View details for DOI 10.1515/crelle-2022-0004

  View details for Web of Science ID 000772596900001

• A model problem for multiplicative chaos in number theory ENSEIGNEMENT MATHEMATIQUE Soundararajan, K., Zaman, A. 2022; 68 (3-4): 307-340

  View details for DOI 10.4171/LEM/1031

  View details for Web of Science ID 000917340200003

• 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

• 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

• 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

• 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