Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let h(p) denote the class number of the real quadratic field formed by adjoining √p, where p is a prime, to the rationals. The Cohen-Lenstra heuristics suggest that the probability that h(p) = k (a given odd positive integer) is given by Cw(k)/k, where C is an explicit constant and w(k) is an explicit arithmetic function. For example,  expect that about 75.45% of the values of h(p) are 1, 12.57% are 3, and 3.77% are 5. Furthermore, a conjecture of Hooley states that H(x):= Σh(p) ∼ x/8 as x → oo, p≤x where the sum is taken over all primes congruent to 1 modulo 4. ,  develop some fast techniques for evaluating h(p) where p is not very large and provide some computational results in support of the Cohen-Lenstra heuristics.  do this by computing h(p) for all p (≡ 1 mod 4) and p < 2 × 10 11 .  also tabulate H(x) up to 2 × 10 11 . 2000 Mathematics Subject Classification: Primary 11R29. Secondary 11Y40. 1998 ACM Computing Classification System: F.2.1.
['Hugh C. Williams', 'Herman J. J. te Riele']
I am writing a research paper on a idea New computations concerning the Cohen-Lenstra heuristics
[{"from": "human", "value": "I am writing a research paper on a idea New computations concerning the Cohen-Lenstra heuristics"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let h(p) denote the class number of the real quadratic field formed by adjoining \u221ap, where p is a prime, to the rationals. The Cohen-Lenstra heuristics suggest that the probability that h(p) = k (a given odd positive integer) is given by Cw(k)/k, where C is an explicit constant and w(k) is an explicit arithmetic function. For example,  expect that about 75.45% of the values of h(p) are 1, 12.57% are 3, and 3.77% are 5. Furthermore, a conjecture of Hooley states that H(x):= \u03a3h(p) \u223c x/8 as x \u2192 oo, p\u2264x where the sum is taken over all primes congruent to 1 modulo 4. ,  develop some fast techniques for evaluating h(p) where p is not very large and provide some computational results in support of the Cohen-Lenstra heuristics.  do this by computing h(p) for all p (\u2261 1 mod 4) and p < 2 \u00d7 10 11 .  also tabulate H(x) up to 2 \u00d7 10 11 . 2000 Mathematics Subject Classification: Primary 11R29. Secondary 11Y40. 1998 ACM Computing Classification System: F.2.1."}]