정수론 학회(2008. 8. 18-21) 참가자 명단

(7월 29일 현재)

순번	성명	소속	발표	숙박날짜	성별
1	양재현	인하대(교수)	oo	18, 19, 20	남
2	최영주	포항공대(교수)		18, 19, 20	여
3	조범규	KAIST(학생)		18, 19, 20	남
4	정호윤	KAIST(학생)		18, 19, 20	남
5	윤동성	KAIST(학생)		18, 19, 20	남
6	엄익선	KAIST(학생)		18, 19, 20	남
7	신동화	KAIST(학생)		18, 19, 20	남
8	박윤경	KAIST(학생)	oo	18, 19, 20	여
9	김남민	KAIST(학생)		18, 19, 20	남
10	구자경	KAIST(교수)		18, 19, 20	남
11	진석호	포항공대(학생)		18, 19, 20	남
12	임수봉	포항공대(학생)	oo	18, 19, 20	남
13	이정연	KAIST(연구원)	oo	18, 19, 20	여
14	김민수	경남대(연구원)	o	마산 자택	남
15	전대열	공주대학교(교수)	oo	18, 19, 20	남
16	이준호	포항공대(학생)	oo	18, 19, 20	남
17	서수길	연세대(교수)	oo	18, 19, 20	남
18	김창헌	서울여대(교수)	oo	18, 19, 20	남
19	이윤진	이화여대(교수)	oo		여
20	박경호	경남대(연구원)	o	마산 자택	남
21	임종렬	포항공대(학생)		18, 19, 20	남
22	강순이	포항공대(연구원)	oo	18, 19, 20	여
23	김현광	포항공대(교수)		18, 19, 20	남
24	안재현	충남대(교수)	o	18, 19, 20 (2인 1실)	부부
25	최소영	동국대(교수)		18, 19, 20	여
26	태재웅	KAIST(학생)		창원 자택	남
27	임보해	중앙대(교수)		18	여
28	Hiranouchi	Kyushu U.	oo	18, 19, 20	남
29	배 성 한	KAIST(교수)		18, 19, 20	남
30	손 진 우	경남대(교수)		마산 자택	남
31	장 승 환	KAIST(연구원)		18, 19, 20	남
32	김 대 열	NIMS(연구원)	oo	18, 19, 20	남

* 일정표

	18	19	20	21
9:45-10:35		서 수 길	이 정 연	김 대 열
10:45-11:35		강 순 이	전 대 열	김 창 헌
11:50-12:40		박 윤 경	T. Hiranouchi	김 민 수
12:40-14:00	등 록	중 식	중 식	폐 회
14:00-14:50	양 재 현	박 경 호	관
15:00-15:50	이 윤 진	임 수 봉	광
16:20-17:10	이 준 호	안 재 현
	Pizza Party		연 회

* 숙소

장소 : 마산시 동성동 315번지 마산 M 호텔 (전화 055-223-0550)

호텔이 경남대에서 좀 떨어져 있습니다.

저녁에는 각자 호텔로 이동합니다. 택시비 3,000 원 정도임.

고속터미널에서 호텔은 택시비 2,000원 남짓임.

(2인 1실)

1. 이정연, 김지영	2. 정호윤, 신동화

3. 진석호, 임수봉	4. 이준호, 임종열

5. 엄익선 윤동성	6. 김대열, 박부성

7. 김남민, 장승환	8. 최소영, 박윤경

교수님들은 1인 1실입니다.

양재현 (인하대학교)

Title: Langlands Functoriality Conjecture

Abstract: Functoriality conjecture is the profound question that was formulated by Robert P. Langlands (1936-  ) in the late 1960s in order to establish non-abelian class field theory and its reciprocity law. The principle of functoriality describes deep relationships among automorphic representations on different reductive groups. Functoriality is the conjecture that automorphic representations on different groups shoud be related in terms of their L-groups and encompasses the local and global Langlands conjectures as special cases. This conjecture states that any L-homomorphism of the L-group of H into the L-group of G should determine a natural lifting of automorphic represenations of H to automorphic representations of G. Here H and G are  connected reductive groups defined over a number field with G quasi-split. Nowadays functoriality is one of the central and influential subjects of present day mathematics.

In this talk,  I discuss the (possibly new) methods to tackle Langlands functoriality conjecture and survey several examples giving some evidences to functoriality.

서수길(연세대)

Title: Z_p extensions and universal norm elements
Abstract: Let K be a number field or local field of chracteristic zero.
We briefly introduce the corelation between the universal norm elements of K
and embedding of a cyclic p-extension of K into a Z_p extension of K.

김창헌(서울여대)

Title: Traces of singular moduli of arbitrary level modular functions
Abstract: (cowork with Dohoon Choi, Daeyeol Jeon and Soon-Yi Kang) Generalizing Zagier's work, Bruinier and Funke recently proved that for modular curves of arbitrary genus, the generating series for the traces of the CM values of a weakly holomorphic modular function is the holomorphic part of a harmonic weak Maass form of weight 3/2. In this talk we show that by adding a suitable linear combination of weight 3/2 Eisenstein series, one can always obtain a generating series that is weakly holomorphic. In particular,  the modular traces of a Hauptmodul on Gamma_0^*(4) are found to be either Fourier coefficents of a weakly holomorphic modular form of weight 3/2 or constant multiples of class numbers.

전대열(공주대)

Title: Families of elliptic curves with prescribed torsion subgroups

Abstract: In this talk we construct some families of elliptic curves with prescribed torsion subgroups over quartic number fields.

이윤진(이화여대)

Title: Class groups of global function fields
Abstract: The problem of determining the structure of class groups of number fields or function fields dates back to Gauss. In this talk we discuss the structure of class groups of global function fields. We focus on the Scholz Theorem (Reflection Theorem) and the explicit construction methods of infinitely many global function fields of a given field extension degree, a prescribed unit rank and guaranteed class group rank. We also discuss some interesting applications of the Scholz Theorem to other research projects.

김민수(경남대)

Title: On q-euler numbers, polynomials and related p-adic integrals

Abstract: In this note we give a new proof of Witt’s formula for q-Euler polynomials and the ordinary Euler numbers, which are related to some known

or new identities involving the Euler numbers polynomials. We give a brief

proof of a classical result due to M. A. Stern, which was recently proved by G.

Liu. Finally we establish an explicit congruence for q-Euler numbers.

김대열(국가수리과학연구소)

Title: Elliptic curves and matrix

Abstract: We state definitions and properties for elliptic curve theory.

And then we will give the relations the number of points of elliptic curve modulo p and hadamard matrix.

강순이(포항공대)

Title:  Mock modular forms that arise from a q-series summation formula
Abstract: We show that some q-series such as universal mock theta functions are linear sums of theta quotient and mock Jacobi forms of weight 1/2, which become holomorphic parts of real analytic modular forms when they are multiplied by suitable powers of q. And we prove that certain linear sums of q-series are weakly holomorphic modular forms of weight 1=2 due to annihilation of mock Jacobi forms or completion by mock Jacobi forms. As an application, we obtain a relation between rank and crank of a partition.

이정연(KAIST)

Title: Class number problems of real quadratic fields for Richaud-Degert type

Abstract: In this talk, we survey Shintani's method to evaluate special values of Hecke's L-function of real quadratic fields. And we will observe the behavior

of Hecke's L-function of real quadratic fields of Richaud-Degert type at s = 0

and deduce the property so-called "Linearity". And we will show relations

between this property and class number problems.

박경호(경남대)

Title: A note on Genocchi numbers and polynomials.
Abstract: In this talk, we study the distribution of Genocchi polynomials. Finally, we construct the Genocchi zeta function which interpolates Genocchi
polynomials at negative intgers.

임수봉(포항공대)

Title: Construction of Jacobi forms associated to indefinite quadratic forms

Abstract: Vigneras constructs non-holomorphic theta functions according to indefinite quadratic forms with arbitrary signature. We use Vigneras theta functions to create examples of non-holomorphic Jacobi forms according to indefinite theta series with two different methds.

김현광, 이준호(포항공대)

Title: Evaluation of the Dedekind zeta functions at s=-1 of simplest quartic field

Abstract: The simplest quartic field is first introduced by A.J.Lazarus. In this paper, we will evaluate zeta function at  s = -1 of the simplest quartic field. We will develop basic properties of the field for the evaluation. We first compute the discriminant, the ring of integers and the different of the field. Finally, we evaluate values of zeta function of the field. For it, we first introduce Sielgel's formula for values of the zeta function of a totally real number field at negative odd integers. Next, we will develop a method of computing sum of divisor function for ideals and will give a full description for a Siegel lattice of the simplest quartic field and compute the values of the Dedekind zeta function of the simplest quartic field.

안재현(충남대)

Title: On the number of restricted irreducible factors of an polynomial in [eqn: F _{} q(T)]

Abstract: Let k = [eqn: F _{} q(T)] and  l be a prime, not equal to chak(k). Let E be a set of monic irreducibles P [eqn: IN] [eqn: F _{} q(T)] with |P|[eqn: ==]1 \p mod {l}. For M [eqn: IN] [eqn: F _{} q(T)], we define [eqn: w _{1} (M)] by the number of irreducible factors P of M with P [eqn: IN] E. For a fixed m, we give a result on the number of monic polynomials M with degree x and [eqn: w _{1} (M)] = m.

조범규, 구자경, 박윤경(KAIST)

Title: On the Ramanujan's cubic continued fraction as modular function

Abstract: We first extend the results of Chan and Baruah on the modular equations of the Ramanujan's cubic continued fraction to all primes p by finding the affine models of modular curves X([eqn: GAMMA]) with [eqn: GAMMA] = [eqn: GAMMA _{1}](6)\[eqn: GAMMA ^{0}](3) and then derive the Kronecker's congruence relations for these modular equations. And, we further show that the singular values of C([eqn: tau]) generate ray class fields modulo 6 over imaginary quadratic fields and find their class polynomials by working with [eqn: {1} over {C( tau )}] as algebraic integers.

T. Hiranouchi (Kyushu U.)
Title: Class field theory of curves over local fields
Abstract: We develop class field theory of curves over local fields
which extends the unramified theory of S. Saito (1985). The class groups which approximate abelian etale fundamental groups of such curves are introduced in the terms of algebraic K-groups by imitating G. Wiesend’s class group.