Glyn Harman
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British mathematician
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Why Is Glyn Harman Influential?
(Suggest an Edit or Addition)According to Wikipedia, Glyn Harman is a British mathematician working in analytic number theory. One of his major interests is prime number theory. He is best known for results on gaps between primes and the greatest prime factor of p + a, as well as his lower bound for the number of Carmichael numbers up to X. His monograph Prime-detecting Sieves was published by Princeton University Press. He has also written a book Metric Number Theory . As well, he has contributed to the field of Diophantine approximation. Harman also proved that there are infinitely many primes whose sum of digits is prime. .
Glyn Harman's Published Works
Published Works
- The Difference Between Consecutive Primes, II (2001) (464)
- ANALYTIC NUMBER THEORY (American Mathematical Society Colloquium Publications 53) (2005) (366)
- Metric number theory (1998) (252)
- Prime-Detecting Sieves (2007) (149)
- Shifted primes without large prime factors (1998) (137)
- The di erence between consecutive primes (1996) (128)
- Trigonometric sums over primes I (1981) (85)
- Diophantine Approximation by Prime Numbers (1982) (82)
- Sums of distances between points of a sphere (1982) (69)
- The Brun-Titchmarsh Theorem on average (1996) (64)
- METRIC DIOPHANTINE APPROXIMATION ON MANIFOLDS (Cambridge Tracts in Mathematics 137) (2000) (56)
- On the distribution of v p modulo one (1983) (49)
- On sums of squares of primes (2006) (42)
- On the Number of Carmichael Numbers up to x (2005) (40)
- On the Distribution of p; Modulo One (1983) (40)
- Primes of the Form [nc] (1995) (38)
- The Values of Additive Forms at Prime Arguments (2006) (37)
- Sums Involving Common Divisors (1986) (33)
- Exponential Sums Formed with the Möbius Function (1991) (33)
- WATT'S MEAN VALUE THEOREM AND CARMICHAEL NUMBERS (2008) (32)
- The Duffin–Schaeffer conjecture with extra divergence II (2008) (32)
- Primes with preassigned digits II (2006) (29)
- On the Distribution of αp Modulo One II (1996) (28)
- INTRODUCTION TO ANALYTIC NUMBER THEORY (Translations of Mathematical Monographs 68) (1989) (27)
- Gaussian primes in Narrow sectors (2001) (26)
- On sums of squares of primes II (2009) (25)
- Metric diophantine approximation with two restricted variables. III: Two prime numbers (1988) (24)
- Products of Small Integers in Residue Classes and Additive Properties of Fermat Quotients (2014) (23)
- A new mean‐value result for Dirichlet L‐functions and polynomials (2004) (22)
- Sieve Methods, Exponential Sums, and their Applications in Number Theory: The Exceptional Set for Goldbach's Problem in Short Intervals (1997) (22)
- Small fractional parts of additive forms (1993) (21)
- The values of ternary quadratic forms at prime arguments (2004) (21)
- Sieve methods, exponential sums, and their applications in number theory : proceedings of a symposium held in Cardiff, July 1995 (1997) (19)
- Short intervals containing numbers without large prime factors (1991) (18)
- SOME CASES OF THE DUFFIN AND SCHAEFFER CONJECTURE (1990) (18)
- Integers without large prime factors in short intervals and arithmetic progressions (1999) (18)
- Metric Diophantine approximation with two restricted variables I. Two square-free integers, or integers in arithmetic progressions (1988) (17)
- On the distribution of ap k modulo one (1991) (16)
- VARIATIONS ON THE KOKSMA-HLAWKA INEQUALITY (2010) (15)
- Trigonometric sums over primes II (1983) (15)
- Distributional Properties of the Largest Prime Factor (2005) (14)
- Diophantine approximation with square-free integers (1984) (14)
- Numbers with a large prime factor (1995) (14)
- Discrepancy Estimates for the Value‐Distribution of the Riemann Zeta‐Function, IV (1994) (13)
- Metrical Theorems on Prime Values of the Integer Parts of Real Sequences (1997) (12)
- On the Erdős-Turán inequality for balls (1998) (11)
- PRIMES IN BEATTY SEQUENCES IN SHORT INTERVALS (2016) (10)
- Diophantine Approximation with a Prime and an Almost‐Prime (1984) (10)
- Diophantine approximation with mild divisibility constraints (2006) (10)
- Primes of the form [cp] (1996) (10)
- Sums of Two Squares in Short Intervals (1991) (10)
- The three primes theorem with almost equal summands (1998) (10)
- Fractional and integral parts of $p^{λ}$ (1991) (9)
- Some theorems in the metric theory of diophantine approximation (1986) (9)
- Metrical Theorems on Restricted Diophantine Approximations to Points on a Curve (2002) (8)
- Approximation of real matrices by integral matrices (1990) (8)
- Simultaneous Diophantine approximation and asymptotic formulae on manifolds (2003) (8)
- Small fractional parts of quadratic forms (1982) (8)
- Diophantine inequalities with mixed powers (1984) (7)
- Almost-primes in short intervals (1981) (7)
- DIOPHANTINE APPROXIMATION WITH GAUSSIAN PRIMES (2019) (7)
- Simultaneous Diophantine Approximation with Primes (1989) (7)
- Primes in short intervals (1982) (7)
- Variants of the Second Borel-Cantelli Lemma and their Applications in Metric Number Theory (2000) (7)
- Numbers with a Large Prime Factor IV (1983) (6)
- The distribution of prime ideals of imaginary quadratic fields (2003) (6)
- Small fractional parts of quadratic and additive forms (1981) (6)
- Metric Diophantine approximation with two restricted variables II: A prime and a square-free integer (1988) (6)
- Numbers badly approximate by fractions with prime denominator (1995) (6)
- Metric Diophantine approximation with two restricted variables. IV. Miscellaneous results (1989) (5)
- Diophantine approximation and prime numbers (1982) (5)
- A Note on The Metrical Theory of Continued Fractions (2000) (5)
- Simultaneous diophantine approximation with square-free numbers (1993) (5)
- NUMBERS WITH A LARGE PRIME FACTOR III (1983) (5)
- Primes of the form [pc] and related questions (1995) (5)
- Metrical Theorems on Fractional Parts of Real Sequences, II (1993) (5)
- On mean values of Dirichlet polynomials (1991) (4)
- On values of n2 + 1 free of large prime factors (2008) (4)
- Diophantine approximation with multiplicative functions (2010) (4)
- Prime-Detecting Sieves (LMS-33) (2012) (4)
- Sequences with bounded logarithmic discrepancy (1990) (4)
- Primes in Intersections of Beatty Sequences (2015) (4)
- On sparsely totient numbers (1991) (4)
- Small remainder of a vector to suitable modulus (1996) (3)
- Metrical theorems on fractional parts of real sequences. (1989) (3)
- On primitive divisors of n^2+b (2007) (3)
- Metrical Theorems on Prime Values of the Integer Parts of Real Sequences II (2001) (3)
- Unbalanced quadratic residues and non-residues (1985) (3)
- The Sequence $x/n$ and its Subsequences (1996) (3)
- PIATETSKI-SHAPIRO PRIME K-TUPLETS (1998) (3)
- Trigonometric sums over primes III (2003) (2)
- Diophantine approximation with almost-primes and sums of two squares (1985) (2)
- Some problems of analytic number theory on arithmetic semigroups (2008) (2)
- Sieve Methods, Exponential Sums, and their Applications in Number Theory: Eratosthenes, Legendre, Vinogradov and beyond (1997) (2)
- Non-linear Diophantine approximation of complex numbers (2002) (1)
- Counting Primes whose Sum of Digits is Prime (2012) (1)
- SMALL FRACTIONAL PARTS OF ADDITIVE FORMS IN PRIME VARIABLES (1995) (1)
- On Averages of Exponential Sums over Primes (1987) (1)
- Weyl ’ s theorem in the measure theory of numbers (2010) (1)
- Number Theory and Polynomials: On primitive divisors of n 2 + b (2008) (1)
- A PROBLEM IN THE METRIC THEORY OF DIOPHANTINE APPROXIMATION (1986) (1)
- THE FRACTIONAL PART OF an k FOR SQUARE-FREE n (1991) (1)
- THE MONTGOMERY–HOOLEY THEOREM IN SHORT INTERVALS (2013) (0)
- Metrical TheoremsonRestrictedDiophantineApproximations to Points ona Curve (2002) (0)
- Towards an arithmetical analysis of the continuum (1995) (0)
- The Duffin–Schaeffer conjecture with extra divergence II (2012) (0)
- Chapter 2. The Vaughan Identity (2012) (0)
- A problem of Hooley in Diophantine approximation (1996) (0)
- Chapter 9. Primes in Almost All Intervals (2012) (0)
- Chapter 11. Generalizing to Algebraic Number Fields (2012) (0)
- On Conjectures of T. Ordowski and Z.W. Sun Concerning Primes and Quadratic Forms (2015) (0)
- Chapter 13. Primes of the Form x3 + 2y3 (2012) (0)
- Chapter 6. An Upper-Bound Sieve (2012) (0)
- DIOPHANTINE APPROXIMATION WITH HARDY–LITTLEWOOD NUMBERS (2019) (0)
- Primes whose sum of digits is prime and metric number theory (2012) (0)
- A Familiar Recurrence Occurs Again (2016) (0)
- Chapter 14. Epilogue (2012) (0)
- Metrical Theorems on the Integer Parts of Real Sequences (2001) (0)
- Chapter 4. The Rosser-Iwaniec Sieve (2012) (0)
- Diophantine approximation with Goldbach numbers (2020) (0)
- Sieve Methods, Exponential Sums, and their Applications in Number Theory: Index of Authors (1997) (0)
- On exponential sums studied by Indlekofer and Kátai (2009) (0)
- REPRESENTING AN INTEGER AS THE SUM OF A PRIME AND THE PRODUCT OF TWO SMALL FACTORS (2020) (0)
- Chapter 8. The Brun-Titchmarsh Theorem on Average (2012) (0)
- Sieve Methods, Exponential Sums, and their Applications in Number Theory: Participants in the Symposium (1997) (0)
- Chapter 3. The Alternative Sieve (2012) (0)
- Chapter 7. Primes in Short Intervals (2012) (0)
- Chapter 12. Variations on Gaussian Primes (2012) (0)
- Chapter 5. Developing the Alternative Sieve (2012) (0)
- Chapter 10. Combination with the Vector Sieve (2012) (0)
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