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**Web Page of the Ottawa-Carleton Number Theory Seminar**

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Year 2017-2018

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**Organizers: **

- Damien Roy: droy@uottawa.ca
- Daniel Fiorilli: Daniel.Fiorilli@uottawa.ca
- Saban Alaca: SabanAlaca@cunet.carleton.ca

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** September 21, 2017, 14:45, U. of Ottawa, room KED B-015 **

**Speaker:** Lucile Devin (U. d'Ottawa)

**Title:** Generalizations of Chebyshev's bias.

**Abstract:**
Following ideas of Rubinstein, Sarnak and Fiorilli, we give a general framework for
the study of prime number races and Chebyshev’s bias attached to general
L-functions L(s) = ∑
_{n≥1 }λ_{f }(n) n^{-s} satisfying natural analytic hypotheses. We put
the emphasis on weakening the required hypotheses such as GRH or linear
independence properties of zeros of L-functions. In particular we establish the
existence of the logarithmic density of the set {x ≥ 2 : ∑
_{p≤x }λ_{f }(p) ≥ 0} conditionally
on a much weaker hypothesis than was previously known. We include applications to
new Chebyshev’s bias phenomena that were beyond the reach of the previously
known cases.

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** October 5, 2017, 14:45, U. of Ottawa, room KED B-015 **

**Speaker:** Luca Ghidelli (U. d'Ottawa)

**Title:** Large gaps in the values of positive-definite diagonal forms

**Abstract:** TBA

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** Seminars from previous years **