Lecture 10, 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, 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, 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, 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, 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, 2019 University of Mississippi

#### Lecture 7, Kannan Soundararajan

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

Extreme values of *L*-functions.

Lecture 6, 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, 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, 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, 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, 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, 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, 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, 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 zerosâ€”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, 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, 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, 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, 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, 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, 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).