## Dilcher, Karl

Compute Distance To:
 Author ID: dilcher.karl Published as: Dilcher, Karl; Dilcher, K.
 Documents Indexed: 117 Publications since 1983, including 1 Book 2 Contributions as Editor Co-Authors: 40 Co-Authors with 91 Joint Publications 934 Co-Co-Authors
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### Co-Authors

 28 single-authored 13 Agoh, Takashi 13 Ericksen, Larry 11 Stolarsky, Kenneth B. 10 Cosgrave, John B. 6 Brown, Jason Ira 6 Skula, Ladislav 5 Vignat, Christophe 4 Manna, Dante V. 3 Ulas, Maciej 2 Al-Shaghay, Abdullah 2 Borwein, Jonathan Michael 2 Borwein, Peter Benjamin 2 Chamberland, Marc 2 Crandall, Richard E. 2 Girstmair, Kurt 2 Jiu, Lin 2 Tomkins, Hayley 1 Anderson, Nancy D. 1 Beck, George 1 Brent, Richard Peirce 1 Chen, Weiyu 1 Haller, Kirk 1 Hessami Pilehrood, Khodabakhsh 1 Hessami Pilehrood, Tatiana 1 Kidwai, Mohammad 1 Knauer, Joshua 1 Lucht, Lutz Gerhard 1 Malloch, Louise 1 Meyer, Jeffrey L. 1 Noble, Rob 1 Nowakowski, Richard Joseph 1 Nulton, James D. 1 Pomerance, Carl Bernard 1 Robins, Sinai 1 Rovnyak, James 1 Rubel, Lee Albert 1 Slavutskii, Ilya Sh. 1 Smyth, Christopher J. 1 Straub, Armin 1 Van Halewyn, C.
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### Serials

 14 Journal of Mathematical Analysis and Applications 10 American Mathematical Monthly 10 Integers 8 The Fibonacci Quarterly 8 Journal of Number Theory 6 Mathematics of Computation 6 Acta Arithmetica 5 International Journal of Number Theory 4 The Ramanujan Journal 4 Journal of Integer Sequences 3 Comptes Rendus Mathématiques de l’Académie des Sciences 2 Discrete Mathematics 2 Periodica Mathematica Hungarica 2 Bulletin of the Polish Academy of Sciences, Mathematics 2 The Electronic Journal of Combinatorics 1 Rocky Mountain Journal of Mathematics 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Annales des Sciences Mathématiques du Québec 1 Canadian Journal of Mathematics 1 Compositio Mathematica 1 Functiones et Approximatio. Commentarii Mathematici 1 Glasgow Mathematical Journal 1 Journal of Approximation Theory 1 Journal of Graph Theory 1 Memoirs of the American Mathematical Society 1 Networks 1 Publicationes Mathematicae Debrecen 1 Transactions of the American Mathematical Society 1 Advances in Applied Mathematics 1 Acta Mathematica Hungarica 1 Aequationes Mathematicae 1 SIAM Journal on Mathematical Analysis 1 Notices of the American Mathematical Society 1 Experimental Mathematics 1 Journal of Algebraic Combinatorics 1 Annals of Combinatorics 1 Analysis (München) 1 CMS Conference Proceedings 1 Queen’s Papers in Pure and Applied Mathematics 1 Communications in Mathematics 1 Research in Number Theory
all top 5

### Fields

 98 Number theory (11-XX) 26 Combinatorics (05-XX) 18 Special functions (33-XX) 16 Functions of a complex variable (30-XX) 8 Field theory and polynomials (12-XX) 4 Approximations and expansions (41-XX) 3 General and overarching topics; collections (00-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Sequences, series, summability (40-XX) 2 Numerical analysis (65-XX) 1 History and biography (01-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Real functions (26-XX) 1 Operator theory (47-XX) 1 Operations research, mathematical programming (90-XX)

### Citations contained in zbMATH Open

100 Publications have been cited 753 times in 542 Documents Cited by Year
Sums of products of Bernoulli numbers. Zbl 0863.11011
Dilcher, Karl
1996
A search for Wieferich and Wilson primes. Zbl 0854.11002
Crandall, Richard; Dilcher, Karl; Pomerance, Carl
1997
Convolution identities and lacunary recurrences for Bernoulli numbers. Zbl 1137.11014
Agoh, Takashi; Dilcher, Karl
2007
Some $$q$$-series identities related to divisor functions. Zbl 0834.05005
Dilcher, Karl
1995
Roots of independence polynomials of well covered graphs. Zbl 0994.05109
Brown, J. I.; Dilcher, K.; Nowakowski, R. J.
2000
Fermat quotients for composite moduli. Zbl 0884.11003
Agoh, Takashi; Dilcher, Karl; Skula, Ladislav
1997
A polynomial analogue to the Stern sequence. Zbl 1117.11017
Dilcher, Karl; Stolarsky, Kenneth B.
2007
Asymptotic behaviour of Bernoulli, Euler, and generalized Bernoulli polynomials. Zbl 0609.10008
Dilcher, Karl
1987
Resultants and discriminants of Chebyshev and related polynomials. Zbl 1067.12001
Dilcher, Karl; Stolarsky, Kenneth B.
2005
Generalized Euler constants for arithmetical progressions. Zbl 0752.11033
Dilcher, Karl
1992
Shortened recurrence relations for Bernoulli numbers. Zbl 1171.11010
Agoh, Takashi; Dilcher, Karl
2009
Zeros of Bernoulli, generalized Bernoulli and Euler polynomials. Zbl 0645.10015
Dilcher, Karl
1988
Reciprocity relations for Bernoulli numbers. Zbl 1204.11048
Agoh, Takashi; Dilcher, Karl
2008
General convolution identities for Bernoulli and Euler polynomials. Zbl 1400.11063
Dilcher, Karl; Vignat, Christophe
2016
Higher-order recurrences for Bernoulli numbers. Zbl 1232.11024
Agoh, Takashi; Dilcher, Karl
2009
Pi, Euler numbers, and asymptotic expansions. Zbl 0711.11009
Borwein, J. M.; Borwein, P. B.; Dilcher, K.
1989
Higher-order convolutions for Bernoulli and Euler polynomials. Zbl 1293.11032
Agoh, Takashi; Dilcher, Karl
2014
Integrals of products of Bernoulli polynomials. Zbl 1215.11014
Agoh, Takashi; Dilcher, Karl
2011
Zeros of the Wronskian of a polynomial. Zbl 0748.30007
Dilcher, Karl; Stolarsky, Kenneth B.
1991
mod $$p^3$$ analogues of theorems of Gauss and Jacobi on binomial coefficients. Zbl 1209.11024
Cosgrave, John B.; Dilcher, Karl
2010
Bernoulli numbers. Bibliography (1713–1990). Enlarged ed. Zbl 0741.11001
1991
On generalized gamma functions related to the Laurent coefficients of the Riemann zeta function. Zbl 0811.33001
Dilcher, Karl
1994
Stern polynomials and double-limit continued fractions. Zbl 1250.11016
Dilcher, Karl; Stolarsky, Kenneth B.
2009
A Pascal-type triangle characterizing twin primes. Zbl 1159.11303
Dilcher, Karl; Stolarsky, Kenneth B.
2005
On a class of nonlinear differential operators acting on polynomials. Zbl 0768.30005
Dilcher, Karl; Stolarsky, Kenneth B.
1992
Wilson quotients for composite moduli. Zbl 1024.11003
Agoh, Takashi; Dilcher, Karl; Skula, Ladislav
1998
Arithmetic properties of Bernoulli-Padé numbers and polynomials. Zbl 1034.11015
Dilcher, Karl; Malloch, Louise
2002
Hyperbinary expansions and Stern polynomials. Zbl 1312.05016
Dilcher, Karl; Ericksen, Larry
2015
Derivatives and fast evaluation of the Tornheim zeta function. Zbl 1433.11106
Borwein, Jonathan M.; Dilcher, Karl
2018
Bernoulli numbers and confluent hypergeometric functions. Zbl 1140.11309
Dilcher, Karl
2002
Recurrence relations for Nörlund numbers and Bernoulli numbers of the second kind. Zbl 1222.11030
Agoh, Takashi; Dilcher, Karl
2010
Divisibility properties of a class of binomial sums. Zbl 1139.11013
Chamberland, Marc; Dilcher, Karl
2006
An introduction to Gauss factorials. Zbl 1300.11004
Cosgrave, John B.; Dilcher, Karl
2011
The multiplicative orders of certain Gauss factorials. Zbl 1218.11003
Cosgrave, John B.; Dilcher, Karl
2011
On multiple zeros of Bernoulli polynomials. Zbl 1167.11009
Dilcher, Karl
2008
Generalized Stern polynomials and hyperbinary representations. Zbl 1429.11055
Dilcher, Karl; Ericksen, Larry
2017
On $$q$$-analogues of double Euler sums. Zbl 1379.11017
Dilcher, K.; Hessami Pilehrood, Kh.; Hessami Pilehrood, T.
2014
On the roots of expected independence polynomials. Zbl 1269.05087
Brown, Jason I.; Dilcher, Karl; Manna, Dante V.
2013
Multiplikationstheoreme für die Bernoullischen Polynome und explizite Darstellungen der Bernoullischen Zahlen. (Multiplication theorems for Bernoulli polynomials and explicit representations of Bernoulli numbers). Zbl 0712.11015
Dilcher, K.
1989
Determinant expressions for $$q$$-harmonic congruences and degenerate Bernoulli numbers. Zbl 1206.11024
Dilcher, Karl
2008
Extensions of the Gauss-Wilson theorem. Zbl 1210.11008
Cosgrave, John B.; Dilcher, Karl
2008
On a Diophantine equation involving quadratic characters. Zbl 0584.10008
Dilcher, Karl
1986
A generalization of Fibonacci polynomials and a representation of Gegenbauer polynomials of integer order. Zbl 0635.33007
Dilcher, Karl
1987
Real Wronskian zero of polynomials with nonreal zeros. Zbl 0715.30008
Dilcher, Karl
1991
Asymptotics of a sequence of sparse binomial-type polynomials. Zbl 1368.05010
Brown, Jason I.; Dilcher, Karl; Manna, Dante V.
2012
The Gauss-Wilson theorem for quarter-intervals. Zbl 1299.11001
Cosgrave, J. B.; Dilcher, K.
2014
The zeros of a certain family of trinomials. Zbl 0751.30007
Dilcher, Karl; Nulton, James D.; Stolarsky, Kenneth B.
1992
Hypergeometric functions and Fibonacci numbers. Zbl 0976.11009
Dilcher, Karl
2000
A new criterion for the first case of Fermat’s last theorem. Zbl 0817.11022
1995
The cube of the Fermat quotient. Zbl 1103.11011
2006
Continued fractions and Stern polynomials. Zbl 1433.11002
Dilcher, Karl; Ericksen, Larry
2018
Polynomials characterizing hyper $$b$$-ary representations. Zbl 1390.05010
Dilcher, Karl; Ericksen, Larry
2018
An explicit form of the polynomial part of a restricted partition function. Zbl 1392.11080
Dilcher, Karl; Vignat, Christophe
2017
On a sequence of sparse binomial-type polynomials. Zbl 1255.05100
Brown, Jason I.; Dilcher, Karl; Manna, Dante V.
2013
A binomial sum related to Wolstenholme’s theorem. Zbl 1241.11016
Chamberland, Marc; Dilcher, Karl
2009
Convolution identities for Stirling numbers of the first kind. Zbl 1219.11035
Agoh, Takashi; Dilcher, Karl
2010
Zeros of iterated integrals of polynomials. Zbl 0843.30007
Borwein, Peter B.; Chen, Weiyu; Dilcher, Karl
1995
Zeros of sections of divergent power series. Zbl 0854.30001
Dilcher, Karl; Rubel, Lee A.
1996
Representations of Stirling numbers of the first kind by multiple integrals. Zbl 1347.11025
Agoh, Takashi; Dilcher, Karl
2015
On a class of iterative recurrence relations. Zbl 0804.11009
Dilcher, Karl
1993
On finite pattern-free sets of integers. Zbl 1137.11015
Dilcher, Karl; Lucht, Lutz G.
2006
Series representations of theta functions in terms of a sequence of polynomials. Zbl 1281.11021
Brown, Jason I.; Dilcher, Karl; Manna, Dante V.
2012
On a congruence of Emma Lehmer related to Euler numbers. Zbl 1325.11004
Cosgrave, John B.; Dilcher, Karl
2013
The maximum modulus of zeros of polynomials. Zbl 0526.30007
Dilcher, Karl
1983
Zeros of the Wronskian of Chebyshev and ultraspherical polynomials. Zbl 0779.30004
Dilcher, Karl; Stolarsky, Kenneth B.
1993
Irreducibility and zeros of generalized Bernoulli polynomials. Zbl 0558.10012
Dilcher, Karl
1984
A generalization of the Eneström-Kakeya theorem. Zbl 0596.30012
Dilcher, Karl
1986
Reducibility and irreducibility of Stern $$(0,1)$$-polynomials. Zbl 1339.11040
Dilcher, Karl; Ericksen, Larry
2014
An extension of Fermat’s little theorem, and congruences for Stirling numbers. Zbl 0986.11011
Dilcher, Karl
2000
Fermat numbers, Wieferich and Wilson primes: computations and generalizations. Zbl 1016.11058
Dilcher, Karl
2001
A role for generalized Fermat numbers. Zbl 1371.11004
Cosgrave, John B.; Dilcher, Karl
2017
Square classes and divisibility properties of Stern polynomials. Zbl 1414.11040
Dilcher, Karl; Tomkins, Hayley
2018
Polynomial analogues of restricted $$b$$-ary partition functions. Zbl 1440.11191
Dilcher, Karl; Ericksen, Larry
2019
Continued fractions and polynomials related to hyperbinary representations. Zbl 1435.11054
Dilcher, Karl; Ericksen, Larry
2018
Infinite products involving Dirichlet characters and cyclotomic polynomials. Zbl 1396.33002
Dilcher, Karl; Vignat, Christophe
2018
Zeros of certain rational approximations to the cosecant. Zbl 0697.30010
Dilcher, Karl; Stolarsky, Kenneth B.
1989
On the roots of strongly connected reliability polynomials. Zbl 1207.05094
Brown, J. I.; Dilcher, K.
2009
Zero-free regions for Bernoulli polynomials. Zbl 0532.30005
Dilcher, Karl
1983
Generalized convolution identities for Stirling numbers of the second kind. Zbl 1210.11028
Agoh, Takashi; Dilcher, Karl
2008
Convolution and reciprocity formulas for Bernoulli polynomials. Zbl 1238.11019
Agoh, Takashi; Dilcher, Karl
2011
Congruences for a class of alternating lacunary sums of binomial coefficients. Zbl 1174.11002
Dilcher, Karl
2007
Three new factors of Fermat numbers. Zbl 1042.11082
Brent, R. P.; Crandall, R. E.; Dilcher, K.; Van Halewyn, C.
2000
Sequences of polynomials whose zeros lie on fixed lemniscates. Zbl 0767.30009
Dilcher, K.; Stolarsky, K. B.
1992
Nested squares and evaluations of integer products. Zbl 0967.11003
Dilcher, Karl
2000
Sums of reciprocals modulo composite integers. Zbl 1295.11030
Cosgrave, John B.; Dilcher, Karl
2013
Congruences for partial sums of reciprocals. Zbl 1397.11004
Al-Shaghay, Abdullah; Dilcher, Karl
2015
Zeros of certain cyclotomy-generated polynomials. Zbl 0726.11015
Dilcher, Karl
1991
Zeros and irreducibility of polynomials with gcd powers as coefficients. Zbl 1308.12001
Dilcher, Karl; Robins, Sinai
2015
The polynomials of Mahler and roots of unity. Zbl 1360.11110
Dilcher, Karl; Ericksen, Larry
2015
Factors and irreducibility of generalized Stern polynomials. Zbl 1339.11036
Dilcher, Karl; Ericksen, Larry
2015
Dedekind sums and uniform distributions. Zbl 1075.11026
Dilcher, Karl; Girstmair, Kurt
2002
Properties of multivariate $$b$$-ary Stern polynomials. Zbl 1473.11063
Dilcher, Karl; Ericksen, Larry
2019
Analogues of the binomial coefficient theorems of Gauss and Jacobi. Zbl 1423.11041
Al-Shaghay, Abdullah; Dilcher, Karl
2016
Nonlinear recurrences related to Chebyshev polynomials. Zbl 1358.30003
Dilcher, Karl; Stolarsky, Kenneth B.
2016
Nonlinear identities for Bernoulli and Euler polynomials. Zbl 1456.11025
Dilcher, Karl
2020
Orthogonal polynomials and Hankel determinants for certain Bernoulli and Euler polynomials. Zbl 1477.11041
Dilcher, Karl; Jiu, Lin
2021
Polynomial analogues of restricted multicolor $$b$$-ary partition functions. Zbl 1466.11070
Dilcher, Karl; Ericksen, Larry
2021
Identities for Bernoulli polynomials related to multiple Tornheim zeta functions. Zbl 1437.11034
Dilcher, Karl; Straub, Armin; Vignat, Christophe
2019
Zeros and irreducibility of Stern polynomials. Zbl 1399.11071
Dilcher, Karl; Kidwai, Mohammad; Tomkins, Hayley
2017
The multiplicative orders of certain Gauss factorials. II. Zbl 1407.11005
Cosgrave, John B.; Dilcher, Karl
2016
Orthogonal polynomials and Hankel determinants for certain Bernoulli and Euler polynomials. Zbl 1477.11041
Dilcher, Karl; Jiu, Lin
2021
Polynomial analogues of restricted multicolor $$b$$-ary partition functions. Zbl 1466.11070
Dilcher, Karl; Ericksen, Larry
2021
Nonlinear identities for Bernoulli and Euler polynomials. Zbl 1456.11025
Dilcher, Karl
2020
Polynomial analogues of restricted $$b$$-ary partition functions. Zbl 1440.11191
Dilcher, Karl; Ericksen, Larry
2019
Properties of multivariate $$b$$-ary Stern polynomials. Zbl 1473.11063
Dilcher, Karl; Ericksen, Larry
2019
Identities for Bernoulli polynomials related to multiple Tornheim zeta functions. Zbl 1437.11034
Dilcher, Karl; Straub, Armin; Vignat, Christophe
2019
Derivatives and fast evaluation of the Tornheim zeta function. Zbl 1433.11106
Borwein, Jonathan M.; Dilcher, Karl
2018
Continued fractions and Stern polynomials. Zbl 1433.11002
Dilcher, Karl; Ericksen, Larry
2018
Polynomials characterizing hyper $$b$$-ary representations. Zbl 1390.05010
Dilcher, Karl; Ericksen, Larry
2018
Square classes and divisibility properties of Stern polynomials. Zbl 1414.11040
Dilcher, Karl; Tomkins, Hayley
2018
Continued fractions and polynomials related to hyperbinary representations. Zbl 1435.11054
Dilcher, Karl; Ericksen, Larry
2018
Infinite products involving Dirichlet characters and cyclotomic polynomials. Zbl 1396.33002
Dilcher, Karl; Vignat, Christophe
2018
Generalized Stern polynomials and hyperbinary representations. Zbl 1429.11055
Dilcher, Karl; Ericksen, Larry
2017
An explicit form of the polynomial part of a restricted partition function. Zbl 1392.11080
Dilcher, Karl; Vignat, Christophe
2017
A role for generalized Fermat numbers. Zbl 1371.11004
Cosgrave, John B.; Dilcher, Karl
2017
Zeros and irreducibility of Stern polynomials. Zbl 1399.11071
Dilcher, Karl; Kidwai, Mohammad; Tomkins, Hayley
2017
General convolution identities for Bernoulli and Euler polynomials. Zbl 1400.11063
Dilcher, Karl; Vignat, Christophe
2016
Analogues of the binomial coefficient theorems of Gauss and Jacobi. Zbl 1423.11041
Al-Shaghay, Abdullah; Dilcher, Karl
2016
Nonlinear recurrences related to Chebyshev polynomials. Zbl 1358.30003
Dilcher, Karl; Stolarsky, Kenneth B.
2016
The multiplicative orders of certain Gauss factorials. II. Zbl 1407.11005
Cosgrave, John B.; Dilcher, Karl
2016
Hyperbinary expansions and Stern polynomials. Zbl 1312.05016
Dilcher, Karl; Ericksen, Larry
2015
Representations of Stirling numbers of the first kind by multiple integrals. Zbl 1347.11025
Agoh, Takashi; Dilcher, Karl
2015
Congruences for partial sums of reciprocals. Zbl 1397.11004
Al-Shaghay, Abdullah; Dilcher, Karl
2015
Zeros and irreducibility of polynomials with gcd powers as coefficients. Zbl 1308.12001
Dilcher, Karl; Robins, Sinai
2015
The polynomials of Mahler and roots of unity. Zbl 1360.11110
Dilcher, Karl; Ericksen, Larry
2015
Factors and irreducibility of generalized Stern polynomials. Zbl 1339.11036
Dilcher, Karl; Ericksen, Larry
2015
Higher-order convolutions for Bernoulli and Euler polynomials. Zbl 1293.11032
Agoh, Takashi; Dilcher, Karl
2014
On $$q$$-analogues of double Euler sums. Zbl 1379.11017
Dilcher, K.; Hessami Pilehrood, Kh.; Hessami Pilehrood, T.
2014
The Gauss-Wilson theorem for quarter-intervals. Zbl 1299.11001
Cosgrave, J. B.; Dilcher, K.
2014
Reducibility and irreducibility of Stern $$(0,1)$$-polynomials. Zbl 1339.11040
Dilcher, Karl; Ericksen, Larry
2014
On the roots of expected independence polynomials. Zbl 1269.05087
Brown, Jason I.; Dilcher, Karl; Manna, Dante V.
2013
On a sequence of sparse binomial-type polynomials. Zbl 1255.05100
Brown, Jason I.; Dilcher, Karl; Manna, Dante V.
2013
On a congruence of Emma Lehmer related to Euler numbers. Zbl 1325.11004
Cosgrave, John B.; Dilcher, Karl
2013
Sums of reciprocals modulo composite integers. Zbl 1295.11030
Cosgrave, John B.; Dilcher, Karl
2013
Asymptotics of a sequence of sparse binomial-type polynomials. Zbl 1368.05010
Brown, Jason I.; Dilcher, Karl; Manna, Dante V.
2012
Series representations of theta functions in terms of a sequence of polynomials. Zbl 1281.11021
Brown, Jason I.; Dilcher, Karl; Manna, Dante V.
2012
Integrals of products of Bernoulli polynomials. Zbl 1215.11014
Agoh, Takashi; Dilcher, Karl
2011
An introduction to Gauss factorials. Zbl 1300.11004
Cosgrave, John B.; Dilcher, Karl
2011
The multiplicative orders of certain Gauss factorials. Zbl 1218.11003
Cosgrave, John B.; Dilcher, Karl
2011
Convolution and reciprocity formulas for Bernoulli polynomials. Zbl 1238.11019
Agoh, Takashi; Dilcher, Karl
2011
mod $$p^3$$ analogues of theorems of Gauss and Jacobi on binomial coefficients. Zbl 1209.11024
Cosgrave, John B.; Dilcher, Karl
2010
Recurrence relations for Nörlund numbers and Bernoulli numbers of the second kind. Zbl 1222.11030
Agoh, Takashi; Dilcher, Karl
2010
Convolution identities for Stirling numbers of the first kind. Zbl 1219.11035
Agoh, Takashi; Dilcher, Karl
2010
Shortened recurrence relations for Bernoulli numbers. Zbl 1171.11010
Agoh, Takashi; Dilcher, Karl
2009
Higher-order recurrences for Bernoulli numbers. Zbl 1232.11024
Agoh, Takashi; Dilcher, Karl
2009
Stern polynomials and double-limit continued fractions. Zbl 1250.11016
Dilcher, Karl; Stolarsky, Kenneth B.
2009
A binomial sum related to Wolstenholme’s theorem. Zbl 1241.11016
Chamberland, Marc; Dilcher, Karl
2009
On the roots of strongly connected reliability polynomials. Zbl 1207.05094
Brown, J. I.; Dilcher, K.
2009
Reciprocity relations for Bernoulli numbers. Zbl 1204.11048
Agoh, Takashi; Dilcher, Karl
2008
On multiple zeros of Bernoulli polynomials. Zbl 1167.11009
Dilcher, Karl
2008
Determinant expressions for $$q$$-harmonic congruences and degenerate Bernoulli numbers. Zbl 1206.11024
Dilcher, Karl
2008
Extensions of the Gauss-Wilson theorem. Zbl 1210.11008
Cosgrave, John B.; Dilcher, Karl
2008
Generalized convolution identities for Stirling numbers of the second kind. Zbl 1210.11028
Agoh, Takashi; Dilcher, Karl
2008
Convolution identities and lacunary recurrences for Bernoulli numbers. Zbl 1137.11014
Agoh, Takashi; Dilcher, Karl
2007
A polynomial analogue to the Stern sequence. Zbl 1117.11017
Dilcher, Karl; Stolarsky, Kenneth B.
2007
Congruences for a class of alternating lacunary sums of binomial coefficients. Zbl 1174.11002
Dilcher, Karl
2007
Divisibility properties of a class of binomial sums. Zbl 1139.11013
Chamberland, Marc; Dilcher, Karl
2006
The cube of the Fermat quotient. Zbl 1103.11011
2006
On finite pattern-free sets of integers. Zbl 1137.11015
Dilcher, Karl; Lucht, Lutz G.
2006
Resultants and discriminants of Chebyshev and related polynomials. Zbl 1067.12001
Dilcher, Karl; Stolarsky, Kenneth B.
2005
A Pascal-type triangle characterizing twin primes. Zbl 1159.11303
Dilcher, Karl; Stolarsky, Kenneth B.
2005
Arithmetic properties of Bernoulli-Padé numbers and polynomials. Zbl 1034.11015
Dilcher, Karl; Malloch, Louise
2002
Bernoulli numbers and confluent hypergeometric functions. Zbl 1140.11309
Dilcher, Karl
2002
Dedekind sums and uniform distributions. Zbl 1075.11026
Dilcher, Karl; Girstmair, Kurt
2002
Fermat numbers, Wieferich and Wilson primes: computations and generalizations. Zbl 1016.11058
Dilcher, Karl
2001
Roots of independence polynomials of well covered graphs. Zbl 0994.05109
Brown, J. I.; Dilcher, K.; Nowakowski, R. J.
2000
Hypergeometric functions and Fibonacci numbers. Zbl 0976.11009
Dilcher, Karl
2000
An extension of Fermat’s little theorem, and congruences for Stirling numbers. Zbl 0986.11011
Dilcher, Karl
2000
Three new factors of Fermat numbers. Zbl 1042.11082
Brent, R. P.; Crandall, R. E.; Dilcher, K.; Van Halewyn, C.
2000
Nested squares and evaluations of integer products. Zbl 0967.11003
Dilcher, Karl
2000
Wilson quotients for composite moduli. Zbl 1024.11003
Agoh, Takashi; Dilcher, Karl; Skula, Ladislav
1998
A search for Wieferich and Wilson primes. Zbl 0854.11002
Crandall, Richard; Dilcher, Karl; Pomerance, Carl
1997
Fermat quotients for composite moduli. Zbl 0884.11003
Agoh, Takashi; Dilcher, Karl; Skula, Ladislav
1997
Sums of products of Bernoulli numbers. Zbl 0863.11011
Dilcher, Karl
1996
Zeros of sections of divergent power series. Zbl 0854.30001
Dilcher, Karl; Rubel, Lee A.
1996
Some $$q$$-series identities related to divisor functions. Zbl 0834.05005
Dilcher, Karl
1995
A new criterion for the first case of Fermat’s last theorem. Zbl 0817.11022
1995
Zeros of iterated integrals of polynomials. Zbl 0843.30007
Borwein, Peter B.; Chen, Weiyu; Dilcher, Karl
1995
On generalized gamma functions related to the Laurent coefficients of the Riemann zeta function. Zbl 0811.33001
Dilcher, Karl
1994
On a class of iterative recurrence relations. Zbl 0804.11009
Dilcher, Karl
1993
Zeros of the Wronskian of Chebyshev and ultraspherical polynomials. Zbl 0779.30004
Dilcher, Karl; Stolarsky, Kenneth B.
1993
Generalized Euler constants for arithmetical progressions. Zbl 0752.11033
Dilcher, Karl
1992
On a class of nonlinear differential operators acting on polynomials. Zbl 0768.30005
Dilcher, Karl; Stolarsky, Kenneth B.
1992
The zeros of a certain family of trinomials. Zbl 0751.30007
Dilcher, Karl; Nulton, James D.; Stolarsky, Kenneth B.
1992
Sequences of polynomials whose zeros lie on fixed lemniscates. Zbl 0767.30009
Dilcher, K.; Stolarsky, K. B.
1992
Zeros of the Wronskian of a polynomial. Zbl 0748.30007
Dilcher, Karl; Stolarsky, Kenneth B.
1991
Bernoulli numbers. Bibliography (1713–1990). Enlarged ed. Zbl 0741.11001
1991
Real Wronskian zero of polynomials with nonreal zeros. Zbl 0715.30008
Dilcher, Karl
1991
Zeros of certain cyclotomy-generated polynomials. Zbl 0726.11015
Dilcher, Karl
1991
Pi, Euler numbers, and asymptotic expansions. Zbl 0711.11009
Borwein, J. M.; Borwein, P. B.; Dilcher, K.
1989
Multiplikationstheoreme für die Bernoullischen Polynome und explizite Darstellungen der Bernoullischen Zahlen. (Multiplication theorems for Bernoulli polynomials and explicit representations of Bernoulli numbers). Zbl 0712.11015
Dilcher, K.
1989
Zeros of certain rational approximations to the cosecant. Zbl 0697.30010
Dilcher, Karl; Stolarsky, Kenneth B.
1989
Zeros of Bernoulli, generalized Bernoulli and Euler polynomials. Zbl 0645.10015
Dilcher, Karl
1988
Asymptotic behaviour of Bernoulli, Euler, and generalized Bernoulli polynomials. Zbl 0609.10008
Dilcher, Karl
1987
A generalization of Fibonacci polynomials and a representation of Gegenbauer polynomials of integer order. Zbl 0635.33007
Dilcher, Karl
1987
On a Diophantine equation involving quadratic characters. Zbl 0584.10008
Dilcher, Karl
1986
A generalization of the Eneström-Kakeya theorem. Zbl 0596.30012
Dilcher, Karl
1986
Irreducibility and zeros of generalized Bernoulli polynomials. Zbl 0558.10012
Dilcher, Karl
1984
The maximum modulus of zeros of polynomials. Zbl 0526.30007
Dilcher, Karl
1983
Zero-free regions for Bernoulli polynomials. Zbl 0532.30005
Dilcher, Karl
1983
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### Cited by 563 Authors

 55 Dilcher, Karl 18 Agoh, Takashi 17 Brown, Jason Ira 12 Komatsu, Takao 11 Simsek, Yilmaz 10 Ericksen, Larry 10 Kim, Minsoo 9 He, Yuan 8 Bayad, Abdelmejid 8 Chen, Zhixiong 8 Hu, Su 8 Srivastava, Hari Mohan 8 Stolarsky, Kenneth B. 8 Tsumura, Hirofumi 7 Adell, José Antonio 7 Mandrescu, Eugen 6 Lekuona, Alberto 6 Levit, Vadim E. 6 Vignat, Christophe 5 Araci, Serkan 5 Cameron, Ben 5 Chu, Wenchang 5 Cosgrave, John B. 5 Du, Xiaoni 5 Guo, Victor J. W. 5 Kim, Daeyeoul 5 Kim, Taekyun 5 Meštrović, Romeo 5 Skula, Ladislav 5 Tran, Khang D. 5 Ulas, Maciej 5 Varona Malumbres, Juan Luis 5 Wang, Weiping 4 Borwein, Jonathan Michael 4 Carballosa, Walter 4 Dağli, Muhammet Cihat 4 Hickman, Carl A. 4 Krasikov, Ilia 4 Moll, Victor Hugo 4 Nowakowski, Richard Joseph 4 Pan, Hao 4 Sun, Zhi-Wei 4 Sun, Zhihong 4 Tauraso, Roberto 4 Zeng, Jiang 3 Andrica, Dorin 3 Bradley, David M. 3 Brent, Richard Peirce 3 Can, Mumun 3 Cangul, Ismail Naci 3 Chatterjee, Tapas 3 Coppo, Marc-Antoine 3 Csordas, George 3 Fu, Amy M. 3 Hessami Pilehrood, Khodabakhsh 3 Hessami Pilehrood, Tatiana 3 Huang, I-Chiau 3 Ismail, Mourad El-Houssieny 3 Jiu, Lin 3 Kamano, Ken 3 Kanemitsu, Shigeru 3 Khurana, Suraj Singh 3 Klaška, Jiří 3 Kuba, Markus F. 3 Mansour, Toufik 3 Nathanson, Melvyn Bernard 3 Navas, Luis M. 3 Ruiz, Francisco J. 3 Seki, Shin-ichiro 3 Sha, Min 3 Sigarreta Almira, José María 3 Torres-Nuñez, Yadira 3 Tyaglov, Mikhail 3 Winterhof, Arne 3 Zhu, Baoxuan 2 Alzer, Horst 2 Andrews, George Eyre 2 Bagdasar, Ovidiu Dumitru 2 Bailey, David Harold 2 Beck, Matthias 2 Blagouchine, Iaroslav V. 2 Bundschuh, Peter 2 Çevik, Ahmet Sinan 2 Chamberland, Marc 2 Chang, Chinghua 2 Coffey, Mark William 2 Coons, Michael 2 Costa, Edgar 2 Crandall, Richard E. 2 Dahlquist, Germund 2 D’Angelo, John P. 2 Genčev, Marian 2 Gupta, Rajat 2 Ha, Chungwei 2 Hancock, Robert 2 Harvey, David I. 2 Hassen, Abdul 2 Hoshino, Richard 2 Jha, Sumit Kumar 2 Jones, Lenny K. ...and 463 more Authors
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### Cited in 164 Serials

 45 Journal of Number Theory 32 The Ramanujan Journal 32 International Journal of Number Theory 27 Journal of Mathematical Analysis and Applications 23 Mathematics of Computation 16 Integers 13 Discrete Mathematics 11 Advances in Difference Equations 10 Applied Mathematics and Computation 8 Discrete Applied Mathematics 8 Functiones et Approximatio. Commentarii Mathematici 8 Proceedings of the American Mathematical Society 8 Integral Transforms and Special Functions 7 Journal of Approximation Theory 7 Advances in Applied Mathematics 7 Acta Mathematica Hungarica 7 The Electronic Journal of Combinatorics 6 Journal of Integer Sequences 6 Research in Number Theory 5 Bulletin of the Australian Mathematical Society 5 Periodica Mathematica Hungarica 5 Journal of Combinatorial Theory. Series B 5 Monatshefte für Mathematik 5 Graphs and Combinatorics 5 Linear Algebra and its Applications 5 Annals of Combinatorics 4 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 4 European Journal of Combinatorics 4 Applied Mathematics Letters 4 Elemente der Mathematik 4 Journal of High Energy Physics 4 Mediterranean Journal of Mathematics 4 Complex Variables and Elliptic Equations 3 Rocky Mountain Journal of Mathematics 3 Acta Arithmetica 3 Compositio Mathematica 3 Czechoslovak Mathematical Journal 3 Journal of Algebra 3 Journal of Combinatorial Theory. Series A 3 Journal of the Mathematical Society of Japan 3 Results in Mathematics 3 Designs, Codes and Cryptography 3 Journal of Mathematical Sciences (New York) 3 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 American Mathematical Monthly 2 Israel Journal of Mathematics 2 Lithuanian Mathematical Journal 2 BIT 2 Glasgow Mathematical Journal 2 Journal of Computational and Applied Mathematics 2 Manuscripta Mathematica 2 Mathematische Zeitschrift 2 Michigan Mathematical Journal 2 Quaestiones Mathematicae 2 Transactions of the American Mathematical Society 2 Aequationes Mathematicae 2 Bulletin of the American Mathematical Society. New Series 2 Bulletin of the Polish Academy of Sciences, Mathematics 2 Applicable Algebra in Engineering, Communication and Computing 2 Experimental Mathematics 2 Journal de Théorie des Nombres de Bordeaux 2 Russian Journal of Mathematical Physics 2 Filomat 2 Finite Fields and their Applications 2 Journal of Difference Equations and Applications 2 Abstract and Applied Analysis 2 Journal of Combinatorial Optimization 2 JP Journal of Algebra, Number Theory and Applications 2 Computational Methods and Function Theory 2 Hacettepe Journal of Mathematics and Statistics 2 Analysis and Applications (Singapore) 2 Fixed Point Theory and Applications 2 Advances in Mathematics of Communications 2 Acta Mathematica Universitatis Ostraviensis 2 Afrika Matematika 2 Communications in Mathematics 2 Journal of Classical Analysis 1 Computers & Mathematics with Applications 1 International Journal of Mathematical Education in Science and Technology 1 Indian Journal of Pure & Applied Mathematics 1 Information Processing Letters 1 Journal d’Analyse Mathématique 1 Journal of Statistical Physics 1 Physica A 1 The Mathematical Intelligencer 1 Advances in Mathematics 1 Archiv der Mathematik 1 Bulletin of the London Mathematical Society 1 Calcolo 1 Colloquium Mathematicum 1 Fasciculi Mathematici 1 International Journal of Mathematics and Mathematical Sciences 1 Inventiones Mathematicae 1 Journal of Graph Theory 1 Journal of the Korean Mathematical Society 1 Journal of Statistical Planning and Inference 1 Mathematische Annalen 1 Mathematics and Computers in Simulation 1 Mathematica Slovaca 1 Networks ...and 64 more Serials
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### Cited in 44 Fields

 402 Number theory (11-XX) 166 Combinatorics (05-XX) 84 Special functions (33-XX) 44 Functions of a complex variable (30-XX) 26 Numerical analysis (65-XX) 21 Field theory and polynomials (12-XX) 17 Real functions (26-XX) 17 Approximations and expansions (41-XX) 17 Probability theory and stochastic processes (60-XX) 16 Harmonic analysis on Euclidean spaces (42-XX) 14 Sequences, series, summability (40-XX) 11 Information and communication theory, circuits (94-XX) 9 Commutative algebra (13-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 8 Dynamical systems and ergodic theory (37-XX) 6 Group theory and generalizations (20-XX) 6 Computer science (68-XX) 5 Associative rings and algebras (16-XX) 5 Several complex variables and analytic spaces (32-XX) 4 History and biography (01-XX) 4 Difference and functional equations (39-XX) 4 Statistical mechanics, structure of matter (82-XX) 4 Operations research, mathematical programming (90-XX) 3 Measure and integration (28-XX) 3 Ordinary differential equations (34-XX) 2 General and overarching topics; collections (00-XX) 2 Algebraic geometry (14-XX) 2 Integral transforms, operational calculus (44-XX) 2 Convex and discrete geometry (52-XX) 2 Algebraic topology (55-XX) 2 Mechanics of particles and systems (70-XX) 2 Quantum theory (81-XX) 2 Relativity and gravitational theory (83-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Abstract harmonic analysis (43-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-XX) 1 Optics, electromagnetic theory (78-XX) 1 Biology and other natural sciences (92-XX) 1 Mathematics education (97-XX)