Research

Analytic Number Theory
Riemann Zeta function, Dirichlet and Hecke L functions
Zero-density and zero-free regions
Distribution of prime numbers
Chebotarev’s density theorem
Explicit Results

• An effective version of Chebotarev's density theorem

with Sourabhashis Das, and Nathan Ng
arXiv:2508.09480, 56 pages, 7 tables (August 2025).

• Conferences for Humans
  with Alia Hamieh, Greg Martin,  and Nathan Ng
  MOSAIC, CMS Notes, June 2025.

• Comparative Prime Number Theory Problem List
  with Alia Hamieh, Greg Martin,  and Nathan Ng
  arxiv.org/pdf/2407.03530, (July 2024).

• Moments of L-functions Problem List
  with Alia Hamieh, Greg Martin,  and Nathan Ng
  arxiv.org/pdf/2405.17800 (May 2024).

• Sharper bounds for the error term in the Prime Number Theorem,
  with Andrew Fiori and Joshua Swidinsky,
  Res. Number Theory 9 (2023), no. 3, Paper No. 63, 19 pp.
  PDF version of Research in Number Theory (August 2023).
  arXiv:2206.12557

• Sharper bounds for the Chebyshev function psi(x)
  with Andrew Fiori and Joshua Swidinsky,
  J. Math. Anal. Appl. 527 (2023), no. 2, Paper No. 127426, 28 pp.
  arxiv.org/abs/2204.02588

• About the necessity of collecting data to improve EDI in mathematics
  MOSAIC, CMS Notes, February 2022.

• Primes in the Chebotarev density theorem for all number fields,
  with Peng-Jie Wong, Appendix "Numerical Verification of the Least Prime in the Chebotarev Density Theorem" by Andrew Fiori.
  J. Number Theory 241 (2022), 700–737.
  arxiv.org/abs/2105.14181

• Sharper bounds for the Chebyshev function 𝜃 (𝑥)
  with Sam Broadbent, Allysa Lumley, Nathan Ng, and Kirsten Wilk,
  Math. Comp. 90 (2021), no. 331, 2281-2315.

• The least prime ideal in the Chebotarev Density Theorem
  with Nathan Ng and Peng Jie Wong,
  Proc. Amer. Math. Soc. 147 (2019), no. 6, 2289-2303.

• Explicit zero density for the Riemann Zeta function
  with Allysa Lumley and Nathan Ng,
  J. Math. Anal. Appl. 465 (2018), no. 1, 22-46.

• Explicit zero-free regions for Dirichlet L-functions
  Mathematika 64 (2018), no. 2, 445-474.

• Short intervals containing primes
  with Allysa Lumley, #A61, Integers 14 (2014), 18p.

• New bounds for psi(x)
  with Laura Faber, Math. Comp. 84 (2015), no. 293, 1339–1357.

• A zero density result for the Riemann zeta function
  Acta Arith. 160 (2013), no. 2, 185–200.

• Explicit zero density theorems for Dedekind Zeta functions
  with Nathan Ng, J. of Number Theory Vol. 132, (2012), no. 4, 748-775.

• Explicit zero-free regions for Dedekind Zeta functions
  Int. J. of Number Theory 2 Vol. 8, No. 1 (2012) 1-23,

• Short effective intervals containing primes in arithmetic progressions and a seven cubes problem
  Math. Comp. 77 (2008), no. 263, 1733-1748.

• Une région explicite sans zéros pour la fonction Zêta de Riemann
  Acta Arith. 117.4 (2005), no. 4, 303-339.

• PhD thesis: Régions explicites sans zéros pour les fonctions L de Dirichlet

• MSc memoir: Sur la distribution des entiers premiers à q

• An explicit Van der Corput result,
  with Natasha Dhiman and Emily Quesada-Herrera, 20 page-preprint.

• An explicit version of Chebotarev density theorem II
  with Sourabhashi Das and Nathan Ng, 36-page preprint.

• Explicit bounds and zero-free regions for Dirichlet $L$-functions
  with Abhay Chadhari (Ohio State), Nicol Leong (UNSW Canberra), and Subham Roy (Montréal).
  IPENT project, 36-page preprint

• Primes in Arithmetic Progression I
  with Allysa Lumley, 47-page preprint.

• Bounds for Mertens Sums
  with Sam Broadbent, Andrew Fiori, Nathan Ng, and Kirsten Wilk, 54-page preprint.

• A zero density result for Dirichlet $L$-functions
  with Allysa Lumley and Nathan Ng, 22-page preprint.

• Generalizations of the Prime Number Theorem
  with Sourabh Das and Allysa Lumley, Birs Team-Up project, 20-page preprint.

• Explicit zero-free regions for all Dirichlet $L$-functions
  with Kübra Benli 33-page preprint.

• 2025
  Speaker and session chair
  33ièmes Journées Arithmétiques, Université  du Luxembourg, June 30-July 4th, 2025.

Invited speaker
Recruitment event for Medicine Hat high school, University of Lethbridge, June 3rd, 2025. 

Plenary Speaker
Alberta Number Theory Days XVI, BIRS (Banff), May 2-4, 2025. \

Invited speaker
Mathematics and Statistics Colloquium, University of Saskatchewan, March 28, 2025. 

Invited speaker
Number Theory Seminar, University of Waterloo ON, March 7, 2025.

• 2024
  Co-organizer
  Scientific Session Celebrating Greg Martin: A Chorus of Contributions to Analytic Number Theory, at the 2024 Winter Meeting of the Canadian Math. Society, Nov.29-Dec.2, 2024, Kwantlen Polytechnic University, Richmond BC.

Invited speaker
Rencontres de théorie analytique et élémentaire des nombres, Institut Henry Poincaré, Paris, November 18, 2024.

Invited speaker
Algèbre, Dynamique et Arithmétique (ADA), Calais, November 7, 2024.

Invited speaker
Dynamique, Arithmétique, Combinatoire (Ernest), Marseille,  October 22, 2024. 

Speaker
SHAD ULethbridge 2024, Lethbridge, July 8, 2024, "Exploring Paths in Number Theory".

Panelist for International Women in Mathematics Day (WIM-CMS event), May 10, online:
https://mathmatters.cms.math.ca/en/article/on-line-panel-for-international-women-in-mathematics-day/

• 2023
  Research group leader:
  Zero-free regions for Dirichlet characters of primes.
  July 2-15, 2023: Inclusive Paths in Explicit Number Theory, CRG Summer School, BIRS UBCO (Kelowna)

Course lecturer:
Zero-free regions close to the real axis, video and notes
July 2-15, 2023: Inclusive Paths in Explicit Number Theory, CRG Summer School, BIRS UBCO (Kelowna)

Panel Organizer and Moderator:
How to be compassionate without burning out, Round-table Discussion.
SPARK Teaching Symposium, ULethbridge, May 3rd, 2023

Plenary speaker (online):
COmbinatorial Number Theory and Connections (CONTACT) II, plenary speaker (online), February 04-05, 2023, An overview of Explicit Number Theory

Public Speaker:
University of Lethbridge Public Professor Series, invited speaker (hybrid), January 26th 2023.
Resilience in Mathematics: YouTube video and Slides.

• 2022
  CRG L-functions Launch event, BIRS (Banff), November 18-20, 2022,
  An overview of Explicit Number Theory:  Math Tube video  and  Slides.
  
  Analytic Number Theory 1 (Math5460/7460), September-December 2022
  Graduate Course offered by ULethbridge and the PIMS Digital Network.
  Course Webpage (restricted access to students).
  
  

• 2021
  SFU Quarantined Number Theory Algebraic Geometry seminar, Primes in the Chebotarev density theorem for all number fields, SFU (Vancouver) in person, Oct 21 2021, Invited Speaker. 

Summer School Inclusive Paths in Analytic Number Theory, online, Aug 23-27 2021, Organizing team and plenary speaker:
Prime Numbers and Riemann Zeta Function (3 lectures).

Amicale de theorie des nombres en hommage a Robert Langlands, CMS 75+1 th anniversary Summer Meeting, online/Ottawa, Ideaux premiers dans le theoreme de densite de Chebotarev pour tous les corps de nombres, June 7-11 2021, Invited Speaker.

• 2020
  Calgary Algebra and Number Theory Seminar, Completely explicit results for primes in Chebotarev density theorem, Jan 30 2020, Invited Speaker.
  
  PIMS-Lethbridge Number Theory and Combinatorics Seminar, Explicit results about primes in Chebotarev's density theorem, Jan. 27 2020, Speaker, MathTube.
  
  

• 2019
  Dec. 2019: Analytic Number Theory Session, CMS Winter Meeting, Toronto, Explicit results about primes in Chebotarev's density theorem.
  
  

• 2018
  Nov. 2018: Association for Women in Math. Colloquium Series, U. of Calgary, Calgary AB, Prime Time.
  
  Jul. 2018: A Celebration of CICMA's postdoctoral program, U. de Montréal, Montréal, QC, Explicit Results about zeros of L-functions and Primes.
  
  Jun. 2018: CMS Summer meeting 2018, Fredericton, NB, A bound for the least prime ideal in the Chebotarev density theorem.
  
  May 2018 & Alberta Math Dialogue, U. of Calgary, Calgary, AB, plenary speaker, Improving explicit approximations on prime counting functions.
  
  

• 2017
  Nov. 2017: Women Scholars Speaker Series, U. of Lethbridge, How did I become a Mathematician?
  
  Mar. 2017: Alberta Number Theory Days (ANTD IX), BIRS, Banff, AB, Explicit Results in prime number theory.  
  Jan. 2017: Algebra and Number Theory Seminar, U. of Mississippi, Oxford, MI, Explicit Results in prime number theory.
  
  Jan. 2017: Joint Mathematics Meeting, MAA Invited Paper Session on L-Functions and Other Animals, Atlanta, GA, New explicit zero density result for the Riemann Zeta Function and consequences for the primes.
  
  

• 2015
  Dec. 2015: Canadian Mathematical Society Winter 2015, Montréal, New bounds for psi(x;q,a).
  
  May 2015: Alberta Math Dialogue, Lethbridge, New bounds for psi(x;q,a).
  
  

• 2014
  Jan. 2014: Joint Mathematics Meeting, AMS Special Session in Analytic Number Theory, Baltimore, Explicit estimates for psi(x).
  
  

• 2012
  Dec. 2012: Canadian Mathematical Society Winter 2012 meeting, Montreal, New explicit bounds for a prime counting function.
  
  

• 2011
  Jun. 2011: Alberta Number Theory Days IV conference (ANTD IV), BIRS, Banff.
  
  May 2011: Analytic Aspects of L-functions and Applications to Number Theory conference,  U. of Calgary.
  
  Apr. 12, 19, 26, 2011: Groupe de travail Analyse harmonique et theorie analytique, Lille I, France.
  
  

• 2010
  May 2010: Groupe de travail Analyse harmonique et theorie analytique, Lille I, France.
  
  

• 2009
  Jul. 2009: Activites Additives et Analytiques Conference, Lille I, France.
  
  Jun. 2009: Fields Institute  Conference in Number Theory, Carleton University, Ottawa. 
  
  Apr. 2009: Math. Colloquium, U. of Calgary.
  
  

• 2008
  Nov. 2008: Women in Numbers workshop, BIRS, Banff.
  
  Oct. 2008: 2008 Fall Western Section Meeting, American Math. Society Meeting, UBC, Vancouver.
  
  Apr. 2008: PIMS/SFU/UBC Number Theory Seminar, Vancouver.
  
  

• 2007
  Feb. 2007: Math. and CS Colloquium, U. of Lethbridge
  
  Feb. 2007: Math. Colloquium, U. of Saskatchewan, Saskatoon.
  
  

• 2006
  Dec. 2006: Connecting Women in Mathematics across Canada conference, Fields Institute, Toronto.
  
  Jul. 2006: Math. Colloquium, U. of Ottawa.
  
  May 2006: Women in Mathematics Program ``Zeta functions all the way'', Institute of Advanced Studies, Princeton, USA.
  
  Jan. 2006: Quebec-Vermont Number Theory Seminar, Montreal.
  
  

• 2005
  May 2005: Conference de theorie des nombres, U. Laval, Quebec.
  
  

• 2004
  Dec. 2004: Canadian Mathematical Society Winter 2004 Meeting, Montreal.
  
  May 2004: Illinois Number Theory Conference, U. of Illinois at Urbana-Champaign, USA.
  
  May 2004: Workshop on Spectral Theory and Automorphic Forms, Centre de Recherches Mathematiques, Montreal.
  
  

• 2003
  Dec. 2003: Number Theory Day Conference, Vancouver.
  
  Dec. 2003: Number Theory Day, Vancouver.
  
  Nov. 2003: Qu\'ebec-Vermont Number Theory Seminar, Montreal.
  
  Jan. 2003:  S\'eminaire Th\'eorie Analytique des Nombres, Institut Elie Cartan, Nancy, France.
  
  Jan. 2003: Seminaire d'Arithmetique, U. Jean Monnet, Saint-Etienne, France.
  
  

• 2002
  Sep. 2002: Seminaire Theorie Algebrique des Nombres LACO, Limoges, France.
  
  Jan. 2002: Colloque Theorie des nombres et applications, Centre International de Rencontres Mathematiques, Marseille, France.
  
  

• 2001
  Oct. 2001: Seminaire Theorie Analytique des Nombres, Institut Henri Poincare, Paris, France.

• 2025
  Panelist:
  WIN7 - "Leading collaborative research projects", Zoom, May 28, 2025.

Host for May 12 Screening of "Journeys of Black Mathematicians: forging resilience", University of Lethbridge, May 16, 2025.

Consultation at the Gender Summit Workshop, (part of NSF's Gender Summit and the Roadmap for Action 2.0), University of Calgary, April 4, 2025.

Panellist at the Navigating Your Careers conference, University of Waterloo, March 8, 2025.

• 2024
  Speaker
  SHAD ULethbridge 2024, Lethbridge, July 8, 2024, "Exploring Paths in Number Theory".
  
  Panelist for International Women in Mathematics Day (WIM-CMS event), May 10, online:
  https://mathmatters.cms.math.ca/en/article/on-line-panel-for-international-women-in-mathematics-day/

Panelist at IGEM Inclusivity Café, September 18, 2024, 1-3pm, UHall Atrium, Lethbridge.

• 2023
  Panel Organizer and Moderator:
  How to be compassionate without burning out, Round-table Discussion.
  SPARK Teaching Symposium, ULethbridge, May 3rd, 2023 

Public Speaker:
University of Lethbridge Public Professor Series, invited speaker (hybrid), January 26th 2023.
Resilience in Mathematics: YouTube video and Slides.

• 2017
  Nov. 2017: Women Scholars Speaker Series, U. of Lethbridge, How did I become a Mathematician?

• Co-organizer:
  Celebrating Greg Martin: A Chorus of Contributions to Analytic Number Theory , Scientific Session at the 2024 Winter Meeting of the Canadian Math. Society, Nov.29-Dec.2, 2024, Kwantlen Polytechnic University, BC.

• Co-organizer:
  Comparative Prime Number Theory Symposium, UBC, Vancouver, June 17-21, 2024 

• Scientific Director:
  Canadian Mathematical Society (CMS) Summer Meeting, Saskatoon, May 31 - June 3, 2024. 

• Co-organizer:
  July 2-15, 2023: Inclusive Paths in Explicit Number Theory, CRG Summer School, BIRS UBCO (Kelowna).
  BIRS page, CRG page (more up to date)

• Co-organizer and panel moderator:
  May 12 - Celebration of Women in Mathematics, ULethbridge/PIMS.
  Videos of Lectures:
  Twelve on the twelfth by Kristine Bauer
  Mathematics for Humanity by Laleh Behjat
  Discussion on the history of the Prime... by Sreerupa Bhattacharjee
  On the quality of the ABC-solutions by Solaleh Bolvardizadeh

• Panel Organizer and Moderator:
  How to be compassionate without burning out, Round-table Discussion.
  SPARK Teaching Symposium, ULethbridge, May 3rd, 2023, 

• Co-organizer:
  CRG L-functions Launch event, BIRS (Banff), November 18-20, 2022
  CRG site, BIRS site.

• Co-organizer:
  CRG workshop on Moments of L-functions, July 25-29 2022, UNBC (Prince-George).

• EDI Forum, CMS Winter meeting, online/SFU (Vancouver), Dec 3-7 2021, Organizing team.

• Workshop Alberta Number Theory Days, hybrid/BIRS (Banff), Nov 5-7, 2021, Organizing team.
  
  

• before 2021: under construction

• Description:
  Analytic number theory focuses on arithmetic questions through the lens of L-functions. These generating series encode arithmetic information and have connections with a host of other mathematical fields, such as algebraic number theory, harmonic analysis, Diophantine approximation, probability, representation theory, and computational number theory. The main focuses of this CRG include moments of L-functions and automorphic forms, explicit results in analytic number theory, and comparative prime number theory.

• CRG Team
  Alia Hamieh (UNBC)
  Habiba Kadiri (ULethbridge)
  Greg Martin (UBC)
  Nathan Ng (ULethbridge)

• CRG News

• Graduate Courses 

• Weekly Seminar 

• Comparative Prime Number Theory Symposium

• Inclusive Paths in Explicit Number theory Summer School

• Workshop Moments of L-functions

• CRG Launch event