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Lehmer
Lehmer is a surname. Notable people with the surname include: * Derrick Norman Lehmer (1867–1938), number theorist who produced tables of prime factors and mechanical devices like Lehmer sieves * Derrick Henry Lehmer (1905–1991), number theorist known for Lucas–Lehmer test, son of D. N. Lehmer and husband of Emma Lehmer * Emma Lehmer (1906–2007), Russian mathematician, known for her work on reciprocity laws, wife of D. H. Lehmer * Kat Lehmer, American film director, writer, actor and artist See also * Derrick Lehmer (other) * Lehmer–Schur algorithm, in mathematics, named after Derrick Henry Lehmer * Lehmer code * Lehmer's conjecture (also known as: ''the Lehmer's Mahler measure problem''), a problem in number theory, after Derrick Henry Lehmer * Lehmer five, named after Dick Lehmer * Lehmer's GCD algorithm, named after Derrick Henry Lehmer, a rather fast GCD algorithm * Lehmer matrix, in mathematics, named after Derrick Henry Lehmer * Lehmer mean, named ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derrick Henry Lehmer
Derrick Henry "Dick" Lehmer (February 23, 1905 – May 22, 1991), almost always cited as D.H. Lehmer, was an American mathematician significant to the development of computational number theory. Lehmer refined Édouard Lucas' work in the 1930s and devised the Lucas–Lehmer test for Mersenne primes. His peripatetic career as a number theorist, with him and his wife taking numerous types of work in the United States and abroad to support themselves during the Great Depression, fortuitously brought him into the center of research into early electronic computing. Early life Lehmer was born in Berkeley, California, to Derrick Norman Lehmer, a professor of mathematics at the University of California, Berkeley, and Clara Eunice Mitchell. He studied physics and earned a bachelor's degree from UC Berkeley, and continued with graduate studies at the University of Chicago. He and his father worked together on Lehmer sieves. Marriage During his studies at Berkeley, Lehmer met Emma Ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lehmer Mean
Lehmer is a surname. Notable people with the surname include: * Derrick Norman Lehmer (1867–1938), number theorist who produced tables of prime factors and mechanical devices like Lehmer sieves * Derrick Henry Lehmer (1905–1991), number theorist known for Lucas–Lehmer test, son of D. N. Lehmer and husband of Emma Lehmer * Emma Lehmer (1906–2007), Russian mathematician, known for her work on reciprocity laws, wife of D. H. Lehmer * Kat Lehmer, American film director, writer, actor and artist See also * Derrick Lehmer (other) * Lehmer–Schur algorithm, in mathematics, named after Derrick Henry Lehmer * Lehmer code * Lehmer's conjecture (also known as: ''the Lehmer's Mahler measure problem''), a problem in number theory, after Derrick Henry Lehmer * Lehmer five, named after Dick Lehmer * Lehmer's GCD algorithm, named after Derrick Henry Lehmer, a rather fast GCD algorithm * Lehmer matrix, in mathematics, named after Derrick Henry Lehmer * Lehmer mean, named ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lucas–Lehmer Primality Test
In mathematics, the Lucas–Lehmer test (LLT) is a primality test for Mersenne numbers. The test was originally developed by Édouard Lucas in 1878 and subsequently proved by Derrick Henry Lehmer in 1930. The test The Lucas–Lehmer test works as follows. Let ''M''''p'' = 2''p'' − 1 be the Mersenne number to test with ''p'' an odd prime. The primality of ''p'' can be efficiently checked with a simple algorithm like trial division since ''p'' is exponentially smaller than ''M''''p''. Define a sequence \ for all ''i'' ≥ 0 by : s_i= \begin 4 & \texti=0; \\ s_^2-2 & \text \end The first few terms of this sequence are 4, 14, 194, 37634, ... . Then ''M''''p'' is prime if and only if :s_ \equiv 0 \pmod. The number ''s''''p'' − 2 mod ''M''''p'' is called the Lucas–Lehmer residue of ''p''. (Some authors equivalently set ''s''1 = 4 and test ''s''''p''−1 mod ''M''''p''). In pseudocode, the test m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emma Lehmer
Emma Markovna Lehmer (''née'' Trotskaia) (November 6, 1906 – May 7, 2007) was an American mathematician known for her work on reciprocity laws in algebraic number theory. She preferred to deal with complex number fields and integers, rather than the more abstract aspects of the theory. Biography Lehmer was born in Samara, Russian Empire, but her father's job as a representative with a Russian sugar company moved the family to Harbin, China in 1910. Emma was tutored at home until the age of 14, when a school was opened locally. She managed to make her way to the US for her higher education. At UC Berkeley, she started out in engineering in 1924, but found her niche in mathematics. One of her professors was Derrick N. Lehmer, the number theorist well known for his work on prime number tables and factorizations. While working for him at Berkeley finding pseudosquares, she met his son, her future husband Derrick H. Lehmer. Upon her graduation summa cum laude with a B.A. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lehmer's Conjecture
Lehmer's conjecture, also known as the Lehmer's Mahler measure problem, is a problem in number theory raised by Derrick Henry Lehmer. The conjecture asserts that there is an absolute constant \mu>1 such that every polynomial with integer coefficients P(x)\in\mathbb /math> satisfies one of the following properties: * The Mahler measure \mathcal(P(x)) of P(x) is greater than or equal to \mu. * P(x) is an integral multiple of a product of cyclotomic polynomials or the monomial x, in which case \mathcal(P(x))=1. (Equivalently, every complex root of P(x) is a root of unity or zero.) There are a number of definitions of the Mahler measure, one of which is to factor P(x) over \mathbb as :P(x)=a_0 (x-\alpha_1)(x-\alpha_2)\cdots(x-\alpha_D), and then set :\mathcal(P(x)) = , a_0, \prod_^ \max(1,, \alpha_i, ). The smallest known Mahler measure (greater than 1) is for "Lehmer's polynomial" :P(x)= x^+x^9-x^7-x^6-x^5-x^4-x^3+x+1 \,, for which the Mahler measure is the Salem number :\m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lehmer Sieve
Lehmer sieves are mechanical devices that implement sieve theory, sieves in number theory. Lehmer sieves are named for Derrick Norman Lehmer and his son Derrick Henry Lehmer. The father was a professor of mathematics at the University of California, Berkeley at the time, and his son followed in his footsteps as a number theorist and professor at Berkeley. A sieve in general is intended to find the numbers which are remainders when a set of numbers are divided by a second set. Generally, they are used in finding solutions of Diophantine equations or to factorization, factor numbers. A Lehmer sieve will signal that such solutions are found in a variety of ways depending on the particular construction. Construction The first Lehmer sieve in 1926 was made using bicycle chains of varying length, with rods at appropriate points in the chains. As the chains turned, the rods would close electrical switches, and when all the switches were closed simultaneously, creating a complete Electrica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derrick Norman Lehmer
Derrick Norman Lehmer (27 July 1867 – 8 September 1938) was an American mathematician and number theorist. Education Lehmer was educated at the University of Nebraska, obtaining his bachelor's degree in 1893 and master's in 1896. His PhD was from the University of Chicago in 1900 for a thesis, ''Asymptotic Evaluation of Certain Totient-Sums,'' under the supervision of E. H. Moore. Career He was appointed instructor in mathematics at the University of California, Berkeley, in 1900 and married Clara Eunice Mitchell on 12 July 1900 in Decatur, Illinois. He was promoted to professor at Berkeley in 1918 and continued to teach there until retiring in 1937. In 1903, he presented a factorization of Jevons's number (8,616,460,799) at the San Francisco Section of the American Mathematical Society on December 19, 1903. He published tables of prime numbers and prime factorization In mathematics, integer factorization is the decomposition of a positive integer into a product of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lehmer Code
In mathematics and in particular in combinatorics, the Lehmer code is a particular way to encode each possible permutation of a sequence of ''n'' numbers. It is an instance of a scheme for numbering permutations and is an example of an inversion table. The Lehmer code is named in reference to D. H. Lehmer, but the code had been known since 1888 at least. The code The Lehmer code makes use of the fact that there are :n!=n\times(n-1)\times\cdots\times2\times1 permutations of a sequence of ''n'' numbers. If a permutation ''σ'' is specified by the sequence (''σ''1, ..., ''σn'') of its images of 1, ..., ''n'', then it is encoded by a sequence of ''n'' numbers, but not all such sequences are valid since every number must be used only once. By contrast the encodings considered here choose the first number from a set of ''n'' values, the next number from a fixed set of values, and so forth decreasing the number of possibilities until the last number for which only a single fixed val ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lehmer Random Number Generator
The Lehmer random number generator (named after D. H. Lehmer), sometimes also referred to as the Park–Miller random number generator (after Stephen K. Park and Keith W. Miller), is a type of linear congruential generator (LCG) that operates in multiplicative group of integers modulo n. The general formula is : X_ = a \cdot X_k \bmod m, where the modulus ''m'' is a prime number or a power of a prime number, the multiplier ''a'' is an element of high multiplicative order modulo ''m'' (e.g., a primitive root modulo ''n''), and the seed ''X'' is coprime to ''m''. Other names are multiplicative linear congruential generator (MLCG) and multiplicative congruential generator (MCG). Parameters in common use In 1988, Park and Miller suggested a Lehmer RNG with particular parameters ''m'' = 2 − 1 = 2,147,483,647 (a Mersenne prime ''M'') and ''a'' = 7 = 16,807 (a primitive root modulo ''M''), now known as MINSTD. Although MINSTD was later criticized by Marsaglia and Sullivan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lucas–Lehmer–Riesel Test
In mathematics, the Lucas–Lehmer–Riesel test is a primality test for numbers of the form with odd . The test was developed by Hans Riesel and it is based on the Lucas–Lehmer primality test. It is the fastest deterministic algorithm known for numbers of that form. For numbers of the form ( Proth numbers), either application of Proth's theorem (a Las Vegas algorithm) or one of the deterministic proofs described in Brillhart–Lehmer–Selfridge 1975 (see Pocklington primality test) are used. The algorithm The algorithm is very similar to the Lucas–Lehmer test, but with a variable starting point depending on the value of . Define a sequence for all by: : u_i = u_^2-2. Then , with , is prime if and only if it divides . Finding the starting value The starting value is determined as follows. * If : if and is even, or and is odd, then divides , and there is no need to test. Otherwise, and the Lucas sequence may be used: we take u_0 = (2+\sqrt)^k+(2-\sqrt) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kat Lehmer
Kat Lehmer (also known as Kathi Lehmer) is an American film director, writer, and actor. Life and career While attending the Pennsylvania Academy of the Fine Arts in Philadelphia where she studied painting, drawing, and sculpture, Lehmer was inspired by the works of an earlier alumnus, David Lynch, to pursue her interest in film making. A subsequent move to New York's Lower East Side exposed her to the underground film movement prevalent in the city during the 1980s where she lived across the street from ABC No Rio,Pierce, D (2007) An Interview with Kathi Lehmer of Trinka Five Films ''Pulpmovies'' a art and punk enclave where underground films were shown. Lehmer started her film production company, Trinka Five Films in 2004. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |