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초록은 발표자 이름 가나다 순서로 찾아보실 수 있습니다.
Title : The number of representations of integers by Bell-type quaternary quadratic forms
Speaker : 권영욱 (성균관대학교)
Abstract : In this talk, we deal with Bell-type quaternary quadratic forms. We will first classify Bell-type forms with class number $\leq 2$, and then we will derive formulas for the representation numbers of each Bell-type form with class number $\leq 2$. This is a joint work with Chang Heon Kim, Kyoungmin Kim, Soonhak Kwon.
Title : Bianchi modular symbols and $p$-adic $L$-functions
Speaker : 권재성 (UNIST)
Abstract : Greenberg's conjecture is a longstanding conjecture in Iwasawa theory, which is related to the $\mu$-invariants of $p$-adic $L$-functions. In this talk, we will discuss the integral $L$-values and $p$-adic $L$-functions of Bianchi modular forms. Also I will give the brief proof of the generation problem of the first homology groups by Bianchi modular symbols. From this, we obtain the result toward the Bianchi modular version of Greenberg's conjecture.
Title : Non-vanishing of modular L-function with quadratic twists
Speaker : 민준휘 (UNIST)
Abstract : In this talk, we introduce a nonvanishing problem of modular L functions, twisted by primitive quadratic characters. Past researches on this problem is geared towards Goldfeld's conjecture, that there exists a positive proportion of fundamental discriminants with L(k,f,\chi_d) is nonzero. We review past improvements on this problem, and briefly talk about how moments of L-values are related with the problem.
Title : Non-vanishing mod p of modular L-values
Speaker : 선해상 (UNIST)
Abstract : Using a dynamical approach, a weak but new result on the residual non-vanishing of modular L-values is obtained by Lee-Sun. In the talk, I will discuss a method to improve the result. This is research in progress.
Title : Subconvexity for weight zero Maass form L-functions in the t aspect
Speaker : 오경원 (UNIST)
Abstract : The main goal of this talk is introduce subconvexity problems for weight zero Maass form. I will give some basic theories about weight zero Maass form and notion of subconvexity bound in the first half of this talk. After that, I explain an expected approach for good subconvexity bound, with simple bessel delta-method and Voronoi summation.
Title : n-level density of the low-lying zeros of primitive Dirichlet L-functions
Speaker : 이윤복 (인천대학교)
Abstract : Katz and Sarnak conjectured that the statistics of low-lying zeros of various family of L-functions matched with the scaling limit of eigenvalues from the random matrix theory. In this paper we confirm this statistic for a family of primitive Dirichlet L-functions matches up with corresponding statistics in the random unitary ensemble, in a range that includes the off-diagonal contribution. To estimate the n-level density of zeros of the L-functions, we use the asymptotic large sieve method developed by Conrey, Iwaniec and Soundararajan. For the random matrix side, a formula from Conrey and Snaith allows us to solve the matchup problem. (This is a joint work with Vorrapan Chandee.)
Title : (C,p)-adic expansions and size of norm of an element in the cone C
Speaker : 이정연 (강원대학교)
Abstract : Let K be a totally real number field, b be a nontrivial ideal of the ring of integer O_K and E_K be the unit group of O_K. For a nonsingular simplicial cone C and rational prime p, we introduce (C,p)-adic expansion of an element in b. By analyzing relations between digits of (C,p)-adic expansion and the action of E_K, we control the size of norm of the element. (This is a part of paper “Cyclotomic fields are generated by cyclotomic Hecke L-values of totally real fields” that is a joint work with Byungheup Jun and Hae-Sang Sun.)
Title : Ranks of elliptic curves over number fields
Speaker : 조재현 (UNIST)
Abstract : For an elliptic curves over Q, we study the analytic ranks of the elliptic curve L-functions over number fields. In particular, we show that the average analytic rank over cyclic extension of prime degree is at most 2 + the analytic rank of E over Q. This result gives some evidence that an elliptic curve is diophantine-stable for cyclic extension of prime degree.
Title : Hecke eigenvalues of Maass forms on GL_2 over any number field
Speaker : 최도훈 (고려대학교)
Abstract : In this talk, I will talk about equidistribution of Hecke eigenvalues of Maass forms of GL_2 over any number field and its application to the Ramanujan conjecture.