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SUMMARY:Akshaa Vatwani (Indian Institute of Technology Gandhinagar)
DTSTART;VALUE=DATE-TIME:20220915T170000Z
DTEND;VALUE=DATE-TIME:20220915T180000Z
DTSTAMP;VALUE=DATE-TIME:20220927T054908Z
UID:crgseminar/1
DESCRIPTION:Title: Joint extreme values of $L$-functions\nby Akshaa Vatwani (Indian In
stitute of Technology Gandhinagar) as part of CRG Weekly Seminars\n\n\nAbs
tract\nWe consider $L$-functions $L_1\,\\ldots\,L_k$ from the Selberg cla
ss having polynomial Euler product and satisfying Selberg's orthonormality
condition. We show that on every vertical line $s=\\sigma+it$ in the comp
lex plane with $\\sigma \\in(1/2\,1)$\, these $L$-functions simultaneously
take "large" values inside a small neighborhood. \nOur method extends to
$\\sigma=1$ unconditionally\, and to $\\sigma =1/2$ on the generalized Rie
mann hypothesis. We also obtain similar joint omega results for arguments
of the given $L$-functions. \nThis is joint work with Kamalakshya Mahatab
and Łukasz Pańkowski.\n
LOCATION:https://researchseminars.org/talk/crgseminar/1/
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BEGIN:VEVENT
SUMMARY:Junxian Li (Mathematisches Institut der Universität Bonn)
DTSTART;VALUE=DATE-TIME:20220922T170000Z
DTEND;VALUE=DATE-TIME:20220922T180000Z
DTSTAMP;VALUE=DATE-TIME:20220927T054908Z
UID:crgseminar/2
DESCRIPTION:Title: Joint value distribution of $L$-functions\nby Junxian Li (Mathemati
sches Institut der Universität Bonn) as part of CRG Weekly Seminars\n\n\n
Abstract\nIt is believed that distinct primitive $L$-functions are “stat
istically independent”. The independence can be interpreted in many diff
erent ways. We are interested in the joint value distributions and their a
pplications in moments and extreme values for distinct $L$-functions. We d
iscuss some large deviation estimates in Selberg and Bombieri-Hejhal’s c
entral limit theorem for values of several $L$-functions. On the critical
line\, values of distinct primitive $L$-functions behave independently in
a strong sense. However\, away from the critical line\, values of distinct
Dirichlet $L$-functions begin to exhibit some correlations.\n\nThis is ba
sed on joint works with Shota Inoue.\n
LOCATION:https://researchseminars.org/talk/crgseminar/2/
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BEGIN:VEVENT
SUMMARY:Youssef Sedrati (Institut Élie Cartan de Lorraine\, Nancy)
DTSTART;VALUE=DATE-TIME:20220929T170000Z
DTEND;VALUE=DATE-TIME:20220929T180000Z
DTSTAMP;VALUE=DATE-TIME:20220927T054908Z
UID:crgseminar/3
DESCRIPTION:Title: Races of irreducible monic polynomials over function fields\nby You
ssef Sedrati (Institut Élie Cartan de Lorraine\, Nancy) as part of CRG We
ekly Seminars\n\n\nAbstract\nChebyshev noticed in 1853 that there is a pre
dominance\, for “most” real numbers $x ≥ 2$\, of the number of prime
s $≤ x$ and congruent to $3$ modulo $4$ over primes $≤ x$ and congruen
t to $1$ modulo $4$. Since then\, several generalizations of this phenomen
on have been studied\, notably in the case of prime number races with thre
e or more competitors by Y. Lamzouri. In this talk\, I will present result
s related to the generalization of Y. Lamzouri’s work in the context of
polynomial rings over finite fields. I will also discuss results concernin
g races of irreducible monic polynomials involving two competitors. In par
ticular\, I will give examples where the races in the function field setti
ng behave differently than in the number field setting.\n
LOCATION:https://researchseminars.org/talk/crgseminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pranendu Darbar (The Norwegian University of Science and Technolog
y)
DTSTART;VALUE=DATE-TIME:20221006T170000Z
DTEND;VALUE=DATE-TIME:20221006T180000Z
DTSTAMP;VALUE=DATE-TIME:20220927T054908Z
UID:crgseminar/4
DESCRIPTION:Title: Multiplicative functions in short intervals\nby Pranendu Darbar (Th
e Norwegian University of Science and Technology) as part of CRG Weekly Se
minars\n\n\nAbstract\nIn this talk\, we are interested in a general class
of multiplicative functions. For a function that belongs to this class\, w
e will relate \nits “short average” to its “long average”. More pr
ecisely\, we will compute the variance of such a function over short inter
vals by using Fourier analysis and by counting rational points on certain
binary forms.\n\nThe discussion is applicable to some interesting multipli
cative functions such as \n\\[\n\\mu_k(n)\, \\\, \\\, \\frac{\\phi(n)}{n}
\, \\\, \\\, \\frac{n}{\\phi(n)}\, \\\, \\\, \\mu^2(n)\\frac{\\phi(n)}{n}
\, \\\,\\\, \\sigma_{\\alpha}(n)\, \\\,\\\,\n (-1)^{\\#\\{p\\\,: \\\, p^k|
n\\}}(n)\,\n\\]\nand many others and it provides various new results and i
mprovements to the previous result in the literature. This is a joint work
with Mithun Kumar Das.\n
LOCATION:https://researchseminars.org/talk/crgseminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chung-Hang (Kevin) Kwan (Columbia University)
DTSTART;VALUE=DATE-TIME:20221020T170000Z
DTEND;VALUE=DATE-TIME:20221020T180000Z
DTSTAMP;VALUE=DATE-TIME:20220927T054908Z
UID:crgseminar/5
DESCRIPTION:by Chung-Hang (Kevin) Kwan (Columbia University) as part of CR
G Weekly Seminars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/crgseminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ayla Gafni (University of Mississippi)
DTSTART;VALUE=DATE-TIME:20221027T170000Z
DTEND;VALUE=DATE-TIME:20221027T180000Z
DTSTAMP;VALUE=DATE-TIME:20220927T054908Z
UID:crgseminar/6
DESCRIPTION:by Ayla Gafni (University of Mississippi) as part of CRG Weekl
y Seminars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/crgseminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiannan Li (Kansas State University)
DTSTART;VALUE=DATE-TIME:20221103T170000Z
DTEND;VALUE=DATE-TIME:20221103T180000Z
DTSTAMP;VALUE=DATE-TIME:20220927T054908Z
UID:crgseminar/7
DESCRIPTION:by Xiannan Li (Kansas State University) as part of CRG Weekly
Seminars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/crgseminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Atul Dixit (Indian Institute of Technology Gandhinagar)
DTSTART;VALUE=DATE-TIME:20221117T180000Z
DTEND;VALUE=DATE-TIME:20221117T190000Z
DTSTAMP;VALUE=DATE-TIME:20220927T054908Z
UID:crgseminar/9
DESCRIPTION:by Atul Dixit (Indian Institute of Technology Gandhinagar) as
part of CRG Weekly Seminars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/crgseminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sanoli Gun (The Institute of Mathematical Sciences)
DTSTART;VALUE=DATE-TIME:20221124T180000Z
DTEND;VALUE=DATE-TIME:20221124T190000Z
DTSTAMP;VALUE=DATE-TIME:20220927T054908Z
UID:crgseminar/10
DESCRIPTION:by Sanoli Gun (The Institute of Mathematical Sciences) as part
of CRG Weekly Seminars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/crgseminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anurag Sahay (University of Rochester)
DTSTART;VALUE=DATE-TIME:20221201T180000Z
DTEND;VALUE=DATE-TIME:20221201T190000Z
DTSTAMP;VALUE=DATE-TIME:20220927T054908Z
UID:crgseminar/11
DESCRIPTION:by Anurag Sahay (University of Rochester) as part of CRG Weekl
y Seminars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/crgseminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shashank Chorge (University of Rochester)
DTSTART;VALUE=DATE-TIME:20221013T170000Z
DTEND;VALUE=DATE-TIME:20221013T180000Z
DTSTAMP;VALUE=DATE-TIME:20220927T054908Z
UID:crgseminar/12
DESCRIPTION:by Shashank Chorge (University of Rochester) as part of CRG We
ekly Seminars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/crgseminar/12/
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