Theory of L-functions, prime numbers and divisors
Theory of L-functions, prime numbers and divisors
批准号:
0555367
负责人:
Kevin Ford
金额:
$14.77万
依托单位国家:
美国
项目类别:
Standard Grant
财政年份:
2006
资助国家:
美国
项目状态:
已结题
起止时间:
2006-06-01 至 2009-05-31
中文摘要
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英文摘要
This project is concerned with investigations into the distributionof zeros of L-functions, prime numbers and divisors of integers.The distribution of prime numbers and zeros of L-functions have longbeen known to be related, but some relations have only recently cometo light. Together with A. Zaharescu and K. Soundararajan, theinvestigator is exploring connections between fractionalparts of imaginary parts of zeros of L-functions, counts ofprime numbers in short intervals, and the pair correlation of zerosof L-functions. A second area of study involves uncoveringsubtle inequities in the distribution of numbers with exactlyk prime factors (k1) in arithmetic progressions, problems intimatelyconnected with the location of the zeros of Dirichlet L-functions.A focus of the research is examining differences between thethe behavior in arithmetic progressions of primes (k=1) and "almostprimes" (k1). Thirdly, the investigator will continue studyinghow the divisors of "typical" and "atypical" integers are distributed.Investigations into the probability theory underlying the study ofdivisors will be a major theme.The positive integers are perhaps the most basic objects inmathematics, and it is important to understand their multiplicativestructure - how they may be written as products, both ofprime numbers and in general. Questions about the distribution ofintegers with a certain multiplicative structure, especially primenumbers, are often very difficult and poorly understood.Several problems of this type are being investigated in this project, withparticular emphasis on the connections with the behavior ofspecial functions called L-functions and with probability andstatistical theory.
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Sieves and primes
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批准号:2301264
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项目类别:Continuing Grant
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资助金额:$37.29万
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财政年份:2023
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负责人:Kevin Ford
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依托单位:
Analytic and Combinatorial Number Theory
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批准号:1902485
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项目类别:Standard Grant
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资助金额:$2.2万
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财政年份:2019
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负责人:Kevin Ford
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依托单位:
Primes, Divisors, and Permutations
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批准号:1802139
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项目类别:Standard Grant
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资助金额:$20.0万
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财政年份:2018
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负责人:Kevin Ford
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依托单位:
Frontiers of Number Theory
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批准号:1501982
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项目类别:Continuing Grant
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资助金额:$36.0万
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财政年份:2015
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负责人:Kevin Ford
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依托单位:
Number Theory at Illinois, June 5-7, 2014
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批准号:1362769
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项目类别:Standard Grant
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资助金额:$2.5万
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财政年份:2014
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负责人:Kevin Ford
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依托单位:
Development of enhanced gene specific technology for the isolation of proteins binding at a single locus in vivo.
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批准号:BB/K013785/1
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项目类别:Research Grant
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资助金额:$15.36万
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财政年份:2013
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负责人:Kevin Ford
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依托单位:
Analytic, probabilistic and combinatorial number theory
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批准号:1201442
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项目类别:Continuing Grant
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资助金额:$28.82万
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财政年份:2012
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负责人:Kevin Ford
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依托单位:
The distribution of prime numbers and products of few primes
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批准号:0901339
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项目类别:Standard Grant
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资助金额:$18.0万
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财政年份:2009
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负责人:Kevin Ford
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依托单位:
Illinois Number Theory Fest
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批准号:0653326
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项目类别:Standard Grant
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资助金额:$1.5万
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财政年份:2007
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负责人:Kevin Ford
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依托单位:
Primes and divisors
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批准号:0301083
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项目类别:Standard Grant
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资助金额:$12.11万
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财政年份:2003
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负责人:Kevin Ford
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依托单位:
Multiplicative Number Theory
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批准号:0196551
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项目类别:Standard Grant
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资助金额:$6.1万
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财政年份:2001
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负责人:Kevin Ford
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依托单位:
Multiplicative Number Theory
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批准号:0070618
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项目类别:Standard Grant
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资助金额:$6.1万
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财政年份:2000
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负责人:Kevin Ford
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依托单位:
国内基金
海外基金
数学物理中精确可解模型的代数方法
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批准号:11771015
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项目类别:面上项目
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资助金额:48.0万元
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批准年份:2017
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负责人:Oleksiy Zhedanov
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依托单位: