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Koukoulopoulos, Dimitrios

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Professeur agregé

Faculté des arts et des sciences - Département de mathématiques et de statistique

André-Aisenstadt local 4163

514 343-6716

Courriels

Cours donnés

  • MAT6111 A - Mesure et intégration

Expertises

 

Encadrement Tout déplier Tout replier

La distribution des zéros des fonctions L Thèses et mémoires dirigés / 2016-08
Comeau-Lapointe, Antoine
Abstract
Selon la philosophie de Katz et Sarnak, la distribution des zéros des fonctions $L$ est prédite par le comportement des valeurs propres de matrices aléatoires. En particulier, le comportement des zéros près du point central révèle le type de symétrie de la famille de fonctions $L$. Une fois la symétrie identifiée, la philosophie de Katz et Sarnak conjecture que plusieurs statistiques associées aux zéros seront modélisées par les valeurs propres de matrices aléatoires du groupe correspondant. Ce mémoire étudiera la distribution des zéros près du point central de la famille des courbes elliptiques sur $mathbb{Q}[i]$. Brumer a effectué ces calculs en 1992 sur la famille de courbes elliptiques sur $mathbb{Q}$. Les nouvelles problématiques reliées à la généralisation de ses travaux vers un corps de nombres seront mises en évidence

Publications choisis Tout déplier Tout replier

Permutations contained in transitive subgroups

S. Eberhard, K. Ford and D. Koukoulopoulos, Permutations contained in transitive subgroups , 33 pages (2016), arXiv:1605.01068, preprint

Sieve weights and their smoothings

A. Granville, D. Koukoulopoulos and J. Maynard, Sieve weights and their smoothings , (2016), , preprint

The frequency of elliptic curve groups over prime finite fields

V. Chandee, C. David, D. Koukoulopoulos and E. Smith, The frequency of elliptic curve groups over prime finite fields , 41 pages (2016), DOI: 10.4153/CJM-2015-013-1, arXiv:1405.6923, Canad. J. Math

\href{https://dx.doi.org/10.1007/978-3-319-22240-0}{Best possible densities, as a consequence of Zhang-Maynard-Tao}

A. Granville, D. M. Kane, D. Koukoulopoulos et R. Lemke Oliver, \href{https://dx.doi.org/10.1007/978-3-319-22240-0}{Best possible densities, as a consequence of Zhang-Maynard-Tao} Analytic Number Theory, In Honor of Helmut Maier's 60th Birthday, Springer, New York, 133-144 (2015), , C. Pomerance et M. Th. Rassias

The mean-value of a product of shifted multiplicative functions and the average number of points of elliptic curves

R. Balasubramanian and S. Giri, The mean-value of a product of shifted multiplicative functions and the average number of points of elliptic curves 157, 37-53 (2015), , J. Number Theory

The cardinality of sumsets: different summands

B. Murphy, E. A. Palsson et G. Petridis, The cardinality of sumsets: different summands 167, no. 4, 375-395 (2015), , Acta Arith.

Best possible densities, as a consequence of Zhang-Maynard-Tao

A. Granville, D. M. Kane, D. Koukoulopoulos and R. Lemke Oliver, Best possible densities, as a consequence of Zhang-Maynard-Tao , 133-144 (2015), arxiv:1410.8198, Analytic Number Theory, In Honor of Helmut Maier's 60th Birthday, Springer, New York

Primes in short arithmetic progressions

D. Koukoulopoulos, Primes in short arithmetic progressions 11, no. 5, 1499-1521 (2015), arXiv:1405.6592, DOI:10.1142/S1793042115400035, Int. J. Number Theory

When the sieve works

A. Granville, D. Koukoulopoulos and K. Matom\"aki, When the sieve works 164, no. 10, 1935-1969 (2015), DOI:10.1215/00127094-3120891, arXiv:1205.0413 , Duke Math. J.

Sieve methods and applications

D. Koukoulopoulos, Sieve methods and applications , In progress (2015), ,

Sums of Euler products and statistics of elliptic curves

C. David, D. Koukoulopoulos and E. Smith, Sums of Euler products and statistics of elliptic curves , 56 pages (2015), arXiv:1510.05935, preprint

Group structures of elliptic curves over finite fields

V. Chandee, C. David, D. Koukoulopoulos and E. Smith, Group structures of elliptic curves over finite fields no. 19, 5230-5248 (2014), DOI: 10.1093/imrn/rnt120, arXiv:1210.3880 , Int. Math. Res. Not. IMRN

On the concentration of certain additive functions

D. Koukoulopoulos, On the concentration of certain additive functions 162, no. 3, 223-241 (2014), arXiv:1111.1040, DOI:10.4064/aa162-3-2 , Acta Arith.

On the number of integers in a generalized multiplication table

D. Koukoulopoulos, On the number of integers in a generalized multiplication table 689, 33-99 (2014), arXiv:1102.3236, DOI:10.1515/crelle-2012-0064 , J. Reine Angew. Math.

The frequency and the structure of large character sums

J. Bober, L. Goldmakher, A. Granville and D. Koukoulopoulos, The frequency and the structure of large character sums , 58 pages (2014), arXiv:1410.8189, preprint

Pretentious multiplicative functions and the prime number theorem for arithmetic progressions

D. Koukoulopoulos, Pretentious multiplicative functions and the prime number theorem for arithmetic progressions 149, no. 7, 1129-1149 (2013), DOI: 10.1112/S0010437X12000802, arXiv:1203.0596, Compos. Math.

On multiplicative functions which are small on average

D. Koukoulopoulos, On multiplicative functions which are small on average 23 no. 5, 1569-1630 (2013), DOI: 10.1007/s00039-013-0235-6, arXiv:1111.2659 , Geom. Funct. Anal.

Arrangements of stars on the American flag

D. Koukoulopoulos, J. Thiel, Arrangements of stars on the American flag 119, no. 6, 443-450 (2012), 10.4169/amer.math.monthly.119.06.443, Amer. Math. Monthly

Localized factorizations of integers

D. Koukoulopoulos, Localized factorizations of integers (3) 101, no. 2, 392-426 (2010), DOI: 10.1112/plms/pdp056, arXiv:0809.1072 , Proc. London Math. Soc.

Divisors of shifted primes

D. Koukoulopoulos, Divisors of shifted primes no. 24, 4585-4627 (2010), DOI: 10.1093/imrn/rnq045, arXiv:0905.0163 , Int. Math. Res. Not. IMRN

A reciprocity theorem for certain hypergeometric series

B. C. Berndt, D. Koukoulopoulos, A reciprocity theorem for certain hypergeometric series 137, 2369-2373 (2009), 10.1090/S0002-9939-09-09777-9, Proc. Amer. Math. Soc.