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Lecture 10, Kannan Soundararajan 2019 University of Mississippi

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 2019 University of Mississippi

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 2019 Texas A&M University

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 2019 Kansas State University

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 2019 University of Mississippi

Lecture 8, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Continuation of Extreme values of L-functions.


Lecture 7, Kannan Soundararajan 2019 University of Mississippi

Lecture 7, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Extreme values of L-functions.


Lecture 6, Kannan Soundararajan 2019 University of Mississippi

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 2019 University of Mississippi

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 2019 Kansas State University

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 2019 Columbia University

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 2019 University of Mississippi

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 2019 University of Mississippi

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 2019 Carleton College

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 â„“-torsion in the class groups of the families of fields.


Landau-Siegel Zeros And Their Illusory Consequences, Kyle Pratt 2019 University of Illinois

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 ...


Lecture 2, Kannan Soundararajan 2019 University of Mississippi

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 2019 University of Mississippi

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.


Arecibo Message, Joshua P. Tan 2019 CUNY La Guardia Community College

Arecibo Message, Joshua P. Tan

Open Educational Resources

This two week assignment asks students to interpret and analyze the 1974 Arecibo Message sent by Drake and Sagan. Week 1 introduces the concepts behind the construction of the message and engages with a critical analysis of the architecture and the contents of the message. Week 2 asks students to develop software in a Jupyter Notebook (available for free from the Anaconda Python Distribution) to interpret messages that were similar to those produced by Drake and Sagan.


Greatest Common Divisor: Algorithm And Proof, Mary K. Flagg 2019 University of St. Thomas - Houston

Greatest Common Divisor: Algorithm And Proof, Mary K. Flagg

Number Theory

No abstract provided.


Extension Of Soft Set To Hypersoft Set, And Then To Plithogenic Hypersoft Set, Florentin Smarandache 2019 University of New Mexico

Extension Of Soft Set To Hypersoft Set, And Then To Plithogenic Hypersoft Set, Florentin Smarandache

Mathematics and Statistics Faculty and Staff Publications

In this paper, we generalize the soft set tothe hypersoft set by transforming the function F into a multi-attribute function. Then we introduce the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set.


Congruence Relations Mod 2 For (2 X 4^T + 1)-Colored Partitions, Nicholas Torello 2019 University of South Carolina

Congruence Relations Mod 2 For (2 X 4^T + 1)-Colored Partitions, Nicholas Torello

Senior Theses

Let p_r(n) denote the difference between the number of r-colored partitions of n into an even number of distinct parts and into an odd number of distinct parts. Inspired by proofs involving modular forms of the Hirschhorn-Sellers Conjecture, we prove a similar congruence for p_r(n). Using the Jacobi Triple Product identity, we discover a much stricter congruence for p_3(n).


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