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Articles 1 - 16 of 16
Full-Text Articles in Physical Sciences and Mathematics
Lecture 10, Kannan Soundararajan
Lecture 10, Kannan Soundararajan
NSF-CBMS Conference: L-functions and Multiplicative Number Theory
Continuation of Fyodorov--Keating conjectures, connections with random multiplicative functions.
Lecture 9, Kannan Soundararajan
Lecture 9, Kannan Soundararajan
NSF-CBMS Conference: L-functions and Multiplicative Number Theory
Fyodorov--Keating conjectures, connections with random multiplicative functions.
The Weyl Bound For Dirichlet L-Functions, Matthew P. Young
The Weyl Bound For Dirichlet L-Functions, Matthew P. Young
NSF-CBMS Conference: L-functions and Multiplicative Number Theory
Abstract: In the 1960's, Burgess proved a subconvexity bound for Dirichlet L-functions. However, the quality of this bound was not as strong, in terms of the conductor, as the classical Weyl bound for the Riemann zeta function. In a major breakthrough, Conrey and Iwaniec established the Weyl bound for quadratic Dirichlet L-functions. I will discuss recent work with Ian Petrow that generalizes the Conrey-Iwaniec bound for more general characters, in particular arbitrary characters of prime modulus.
Extension Of A Positivity Trick And Estimates Involving L-Functions At The Edge Of The Critical Strip, Xiannan Li
Extension Of A Positivity Trick And Estimates Involving L-Functions At The Edge Of The Critical Strip, Xiannan Li
NSF-CBMS Conference: L-functions and Multiplicative Number Theory
Updated schedule
Abstract: I will review an old trick, and relate this to some modern results involving estimates for L-functions at the edge of the critical strip. These will include a good bound for automorphic L-functions and Rankin-Selberg L-functions as well as estimates for primes which split completely in a number field.
Lecture 8, Kannan Soundararajan
Lecture 8, Kannan Soundararajan
NSF-CBMS Conference: L-functions and Multiplicative Number Theory
Continuation of Extreme values of L-functions.
Lecture 7, Kannan Soundararajan
Lecture 7, Kannan Soundararajan
NSF-CBMS Conference: L-functions and Multiplicative Number Theory
Extreme values of L-functions.
Lecture 6, Kannan Soundararajan
Lecture 6, Kannan Soundararajan
NSF-CBMS Conference: L-functions and Multiplicative Number Theory
Continuation of Progress towards moment conjectures -- upper and lower bounds.
Lecture 5, Kannan Soundararajan
Lecture 5, Kannan Soundararajan
NSF-CBMS Conference: L-functions and Multiplicative Number Theory
Progress towards moment conjectures -- upper and lower bounds.
High Moments Of L-Functions, Vorrapan Chandee
High Moments Of L-Functions, Vorrapan Chandee
NSF-CBMS Conference: L-functions and Multiplicative Number Theory
Abstract: Moments of L-functions on the critical line (Re(s) = 1/2) have been extensively studied due to numerous applications, for example, bounds for L-functions, information on zeros of L-functions, and connections to the generalized Riemann hypothesis. However, the current understanding of higher moments is very limited. In this talk, I will give an overview how we can achieve asymptotic and bounds for higher moments by enlarging the size of various families of L-functions and show some techniques that are involved.
Moments Of Cubic L-Functions Over Function Fields, Alexandra Florea
Moments Of Cubic L-Functions Over Function Fields, Alexandra Florea
NSF-CBMS Conference: L-functions and Multiplicative Number Theory
Abstract: I will talk about some recent work with Chantal David and Matilde Lalin about the mean value of L-functions associated to cubic characters over F_q[t] when q=1 (mod 3). I will explain how to obtain an asymptotic formula which relies on obtaining cancellation in averages of cubic Gauss sums over functions fields. I will also talk about the corresponding non-Kummer case when q=2 (mod 3) and I will explain why this setting is somewhat easier to handle than the Kummer case, which allows us to prove some better results.
Lecture 4, Kannan Soundararajan
Lecture 4, Kannan Soundararajan
NSF-CBMS Conference: L-functions and Multiplicative Number Theory
Larger values of L-functions on critical line -- moments, conjectures.
Lecture 3, Kannan Soundararajan
Lecture 3, Kannan Soundararajan
NSF-CBMS Conference: L-functions and Multiplicative Number Theory
Continuation of Selberg's central limit theorem and analogues in families of L-functions (typical size of values on critical line).
An Effective Chebotarev Density Theorem For Families Of Fields, With An Application To Class Groups, Caroline Turnage-Butterbaugh
An Effective Chebotarev Density Theorem For Families Of Fields, With An Application To Class Groups, Caroline Turnage-Butterbaugh
NSF-CBMS Conference: L-functions and Multiplicative Number Theory
This talk will present an effective Chebotarev theorem that holds for all but a possible zero-density subfamily of certain families of number fields of fixed degree. For certain families, this work is unconditional, and in other cases it is conditional on the strong Artin conjecture and certain conjectures on counting number fields. As an application, we obtain nontrivial average upper bounds on ℓ-torsion in the class groups of the families of fields.
Landau-Siegel Zeros And Their Illusory Consequences, Kyle Pratt
Landau-Siegel Zeros And Their Illusory Consequences, Kyle Pratt
NSF-CBMS Conference: L-functions and Multiplicative Number Theory
Updated time
Abstract: Researchers have tried for many years to eliminate the possibility of LandauSiegel zeros—certain exceptional counterexamples to the Generalized Riemann Hypothesis. Often one thinks of these zeros as being a severe nuisance, but there are many situations in which their existence allows one to prove spectacular, though illusory, results. I will review some of this history and some of these results. In the latter portion of the talk I will discuss recent work, joint with H. M. Bui and Alexandru Zaharescu, in which we show that the existence of Landau-Siegel zeros has implications for the behavior of Dirichlet …
Lecture 2, Kannan Soundararajan
Lecture 2, Kannan Soundararajan
NSF-CBMS Conference: L-functions and Multiplicative Number Theory
Selberg's central limit theorem and analogues in families of L-functions (typical size of values on critical line).
Lecture 1, Kannan Soundararajan
Lecture 1, Kannan Soundararajan
NSF-CBMS Conference: L-functions and Multiplicative Number Theory
Introduction to the rest of lectures + value distribution of L-functions away from critical line.