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SUMMARY:Peng Gao (BUAA)
DTSTART:20201124T080000Z
DTEND:20201124T090000Z
DTSTAMP:20260424T222402Z
UID:numsjtu/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/numsj
 tu/1/">The fourth moment of quadratic Hecke $L$-functions in $\\mathbb{Q}(
 i)$</a>\nby Peng Gao (BUAA) as part of SJTU number theory seminar\n\n\nAbs
 tract\nIn this talk\, we study the fourth moment of central values of quad
 ratic Hecke $L$-functions in the Gaussian field. We show an asymptotic for
 mula valid under the generalized Riemann hypothesis (GRH). We also present
  precise lower bounds unconditionally and upper bounds under GRH for highe
 r moments of the same family.\n
LOCATION:https://stable.researchseminars.org/talk/numsjtu/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chang Heon Kim (SKKU)
DTSTART:20210128T070000Z
DTEND:20210128T080000Z
DTSTAMP:20260424T222402Z
UID:numsjtu/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/numsj
 tu/2/">Hecke system of harmonic Maass functions and applications to modula
 r curves of higher genera</a>\nby Chang Heon Kim (SKKU) as part of SJTU nu
 mber theory seminar\n\n\nAbstract\nThe unique basis functions $j_m$ of the
  form $q^{-m}+O(q)$ for the space of weakly holomorphic modular functions 
 on the full modular group form a Hecke system. This feature was a critical
  ingredient in proofs of arithmetic properties of Fourier coefficients of 
 modular functions and denominator formula for the Monster Lie algebra.\n\n
 In this talk\, we consider the basis functions of the space of harmonic we
 ak Maass functions of an arbitrary level\, which generalize $j_m$\, and sh
 ow that they form a Hecke system as well. As applications\, we\nestablish 
 some divisibility properties of Fourier coefficients of weakly holomorphic
  modular forms on modular curves of genus $\\ge1$. Furthermore\, we presen
 t a general duality relation that these modular forms\nsatisfy.\nThis is a
  joint work with Daeyeol Jeon and Soon-Yi Kang.\n\nZoom ID: 955 492 12478\
 , password: 120205\n
LOCATION:https://stable.researchseminars.org/talk/numsjtu/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Detchat Samart (Burapha University)
DTSTART:20210407T070000Z
DTEND:20210407T080000Z
DTSTAMP:20260424T222402Z
UID:numsjtu/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/numsj
 tu/3/">Mahler measures of algebraic varieties: Results and experiments</a>
 \nby Detchat Samart (Burapha University) as part of SJTU number theory sem
 inar\n\nLecture held in zoom: 658 593 56935.\n\nAbstract\nThe (logarithmic
 ) Mahler measures of an $n$-variable polynomial $P$ is defined as the arit
 hmetic mean of $\\log |P|$ over the $n$-torus. Despite its purely analytic
  formulation\, Mahler measure is known to have a deep connection with the 
 arithmetic of the corresponding algebraic variety via $L$-functions\, than
 ks to work of Deninger\, Boyd\, Bertin\, and many others. There are severa
 l known results and conjectures in the literature\nrelating Mahler measure
 s to special $L$-values of Dirichlet series\, elliptic curves\, $K3$ surfa
 ces\, and modular forms. In this talk\, we will give a survey of recent re
 sults in this research direction from both\ntheoretical and experimental p
 erspectives.\n\nzoom: 658 593 56935\, password: the first 6 digits of $\\z
 eta(3)$\n
LOCATION:https://stable.researchseminars.org/talk/numsjtu/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:YiFan Yang (National Taiwan University)
DTSTART:20210106T070000Z
DTEND:20210106T080000Z
DTSTAMP:20260424T222402Z
UID:numsjtu/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/numsj
 tu/4/">Differential equations satisfied by modular forms</a>\nby YiFan Yan
 g (National Taiwan University) as part of SJTU number theory seminar\n\n\n
 Abstract\nA classical result known since the nineteenth century asserts th
 at if $F(z)$ is a modular form of weight $k$ and $t(z)$ is a nonconstant m
 odular function on a Fuchsian subgroup of $SL(2\,\\mathbb{R})$ of the firs
 t kind\, then $F(z)\, zF(z)\,... z^kF(z)$\, as (multi-valued) functions of
  $t$\, are solutions of a $k+1$-st order linear ordinary differential equa
 tions with algebraic functions of t as coefficients. This result constitut
 es one of the main sources of applications of modular forms to other branc
 hes of mathematics. In this talk\, we will give a quick overview of this c
 lassical result and explain some of its applications in number theory.\n
LOCATION:https://stable.researchseminars.org/talk/numsjtu/4/
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