山东大学研究生导师介绍-----展涛
zhan taoindex
address
education
overseas research
research interest
positions
publications
delivered talks
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current address
tao zhan, ph.dprofessordepartment of mathematicsshandong university250100 jinan, shandongpr chinatel: ++86/531/8906961 with extension 2953fax: ++86/531/8902167email: zhantao@sdu.edu.cn
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education
b.s: shandong university (1983)
m.s: shandong university (1995), supervisor: professor chengdong pan
ph.d: shandong university (1987), supervisor: professor chengdong pan
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overseas research experience
1991-1992: institute of mathematics, university of freiburg in germany
research fellow supported by the alexander von humboldt foundation in germany.
feb-july 1996: department of mathematics, the university of hong kong research fellow supported by the croucher foundation in hong kong.
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research interests
goldbach conjecture and other additive problems;
exponential sums over prime variables;
bombieri-vinogradov type mean value theoreoms;
riemann zeta function and dirichlet l-function.
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positions
vice-president of shandong university
chairman of shandong mathematics society
member of the standing committee of all china youth association
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selected publications
on the distribution of k-full integers
science in china(a), vol.32 (1989), 20-37.
on the distribution of k-full integers ii
chin. adv. math., vol.17, no.1(1988), 94-96.
on the error function of square-full integers
chin. ann. math.(ser b), vol.10, no.2(1989), 227-235.
bombieri"s theorem in short intervals
acta math. sinica (new series), vol.5, no.1(1989), 37-47.
on the representation of large odd integers as sum of three almost equal primes
acta math. sinica (new series), vol.7, no.3(1991), 259-272.
davenport"s theorem in short intervals
chin. ann. math.(ser b),vol.12, no.4(1991), 421-431.
on the mean square of dirichlet l-functions
acta math. sinica (new series), vol.8, no.2(1992), 204-224.
on the distribution of integers with a fixed number of prime factors
math. z., vol.213 (1993), 133-147 (joint with dieter wolke).
some remarks on the binary goldbach problem
arch. math., vol.16 (1993), 241-249 (joint with dieter wolke).
a generalization of the goldbach-vinogradov theorem
acta arith., vol.71 (1995), 95-106.
a generalization of bombieri"s theorem and its applications
science in china (series a), vol. 38, no.12 (1995), 1432-1443 (joint with jiafa lin).
some almost-all results concerning the sapiro primes
chin. ann. math.(ser b), vol.17, no.3 (1996), 279-288 (joint with dietmar fischer).
on sum of five almost equal prime squares
acta arith., vol.77 (1996), 369-383 (joint with jianya liu).
exponential sums involving the mobius function
indag. mathem., new series, vol.7, no.2 (1996), 271-278 (joint with jianya liu).
a bombieri type theorem of exponential sums with prime variable
chin. sci. bull., vol.41, no.3 (1996), 193-195 (joint with jianya liu).
estimation of exponential sums over primes in short intervals ii
analytic number theory, proceedings of a conference in honor of heini halberstam, edited by b.c. berndt, h.g. diamond & a.j. hildebrand, 571-606, birkhauser 1996 (joint with jianya liu).
the ternary goldbach problem in arithmetic progressions
acta arith., vol.82, no.3(1997), 197-227 (joint with jianya liu).
estimation of exponential sums over primes in short intervals i
monatash. math.(accepted, joint with jianya liu).
the goldbach problem with primes in arithmetic progressions
london math. soc. lecture notes 247, analytic number theory, edited by yoichi motohashi, cambridge university press, 1997 , 227-251 (joint with ming-chit liu)
on a theorem of hua
arch. math., vol.69(1997),375-390 (joint with jianya liu).
on sum of five almost equal prime squares
science in china (accepted, joint with jianya liu).
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talks delivered at international conferences
the goldbach-vinogradov theorem in short intervals
international conference in number theory, oberwohlfach 1991.
some remarks on the binary goldbach problem
international conference in number theory, marseille, luminy 1992.
on integers with a fixed number of prime factors
annual meeting of the germany mathematics society, berlin 1992.
on the distribution of a special class of integers
international conference in number theory, hong kong 1993.
estimation of non-linear exponential sums over primes
international conference in number theory in honor of professor heini halberstam, urbana-champaign 1995.
the goldbach problem with primes in arithmetic progressions
international conference in number theory, kyoto 1996.
on some problems in the additive prime number theory
workshop and conference in number theory, hong kong 1996.
on sum of prime squares
international conference in number theory in honor of professor andrej schinzel, zakopane, poland 1997.
the goldbach-vinogradov theorem with restrictions on prime variables
101 years of prime number theorem, ulm, germany 1997.
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