混乱生活
发表于 2025-3-23 11:13:12
Periodic Arithmetical Functions and Gauss Sums,Let . be a positive integer. An arithmetical function . is said to be . (or .) if .for all integers .. If . is a period so is . for any integer . > 0. The smallest positive period of . is called the ..
endocardium
发表于 2025-3-23 16:20:40
Primitive Roots,Let . and . be relatively prime integers, with . ≥ 1, and consider all the positive powers of ..We know, from the Euler — Fermat theorem, that a. ≡ 1 (mod .). However, there may be an earlier power a. such that a. ≡ 1 (mod .). We are interested in the smallest positive . with this property.
Anecdote
发表于 2025-3-23 20:04:20
http://reply.papertrans.cn/48/4735/473401/473401_13.png
Nonporous
发表于 2025-3-24 01:43:15
Analytic Proof of the Prime Number Theorem,The prime number theorem is equivalent to the statement . where .(.) is Chebyshev’s function,
少量
发表于 2025-3-24 06:21:10
http://reply.papertrans.cn/48/4735/473401/473401_15.png
projectile
发表于 2025-3-24 07:00:47
Dirichlet Series and Euler Products,He deduced this from the fact that the zeta function .(.), given by.for real . > 1, tends to 0o as . → 1. In 1837 Dirichlet proved his celebrated theorem on primes in arithmetical progressions by studying the series.where . is a Dirichlet character and . > 1.
BOOST
发表于 2025-3-24 14:33:33
http://reply.papertrans.cn/48/4735/473401/473401_17.png
暴发户
发表于 2025-3-24 17:37:19
Introduction to Analytic Number Theory978-1-4757-5579-4Series ISSN 0172-6056 Series E-ISSN 2197-5604
Hamper
发表于 2025-3-24 19:05:56
http://reply.papertrans.cn/48/4735/473401/473401_19.png
狼群
发表于 2025-3-24 23:41:39
http://reply.papertrans.cn/48/4735/473401/473401_20.png